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Physics > Section 9 - Gravitational and Electric Fields > Flashcards

Section 9 - Gravitational and Electric Fields Flashcards

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1
Q

What is a force field?

A

A region where an object will experience a non-contact force.

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2
Q

What do force fields cause?

A

Interactions between objects or particles.

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3
Q

What is a gravitational field?

A

A region where objects with mass will experience an attractive force.

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4
Q

How can a force field be represented?

A

Using field lines (or “lines of force”) that show the direction of the force that would be exerted on an object in a given position.

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5
Q

How are field lines used to show the strength of a field?

A

The further apart the lines are, the weaker the field.

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6
Q

Describe the gravitational field of the Earth.

A
  • It is radial, so the field lines meet at the centre of the Earth like a spiderweb
  • Close to the surface, the field can be considered almost uniform since the field lines are almost parallel and equally spaced
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7
Q

What does Earths radial field look like?

A
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8
Q

What will the force experienced by an object in a gravitational field always be?

A

Attractive

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9
Q

the gravitational force between two point masses (Newton’s Law of Gravitation) is found on the data sheet. what do the symbols stand for?

F = Gm₁m₂ / r²

A

F = Gm₁m₂ / r²

Where:
• F = Force (N)
• G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
• m = Mass (kg)
• r = Distance between centres of two point masses (m)

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10
Q

Where do we assume all the weight is concentrated for objects that experience a force?

A

In the centre - e.g. uniform spheres

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11
Q

When talking about a mass of an object in orbit, what is M and what is m

A 
M = mass of larger object
m = mass of smaller, orbiting object
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12
Q

How do you get the equation for speed of an object orbiting a larger object (e.g. a planet)? not found on data sheet

A

GMm/r² = mv² /r.

equating centripetal force equation to gravity equation

The smalls m’s cancel and one of the r’s cancel.

V = √GM/r

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13
Q

What is the equation of the time period of earths orbit?

A

Time = distance/speed.

T = 2πr/v

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14
Q

What type of law is Newton’s Law of Gravitation and how can this be symbolised?

A
  • Inverse square law

* F ∝ 1 / r²

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15
Q

If the distance between 2 point masses is doubled, what happens to the magnitude of the gravitational force between them?

A

It is one quarter of the original.

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16
Q

What has a bigger impact on the size of the gravitational force, the distance between them or the mass?

A
  • The distance

* This can be seen with Newton’s Law of Gravitation

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17
Q

In gravitational calculations, what is G?

A
  • The gravitational constant
  • It is used in some equations
  • 6.67 x 10^-11 Nm²/kg²
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18
Q

What is gravitational field strength?

A

• The force per unit mass exerted at a given position in a gravitational field.
OR
• The acceleration of a mass in a gravitational field.

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19
Q

What is the symbol for gravitational field strength?

A

g

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20
Q

What are the units for gravitational field strength?

A

N/kg or m/s²

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21
Q

What is the equation that defines gravitational field strength?

A

g = F / m

Where:
• g = Gravitational field strength (N/kg)
• F = Force (N)
• m = Mass (kg)

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22
Q

Is the value of g constant throughout a field?

A

No, its value depends on the where you are in the field.

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23
Q

What is the value of g at the Earth’s surface?

A

9.81 N/kg (or m/s²)

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24
Q

Because F is a vector, where is the direction of the force always towards? (common sense)

A

Towards the the centre of the mass which caused the gravitational force

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25
Q

Is g constant around the world?

A

The gravitational field is almost uniform at the Earth’s surface, so you can assume that g is a constant as long as you don’t go too high above the Earth’s surface.

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26
Q

The force on M1 due to M2 to equal and opposite to the force on…

A

M2 due to M1

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27
Q

In a radial field, how does g vary with the radius from the centre of the mass?

A

g is inversely proportional to r²

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28
Q

When we (humans) fall to the ground, why don’t we notice Earth’s acceleration towards us?

A
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29
Q

Describe the gravitational field around a point mass.

A

Radial

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30
Q

Give the equation for g around a point mass.

A

g = GM / r²

OR

g = -ΔV / Δr

Where:
• g = Gravitational field strength (N/kg)
• G = Gravitational constant (Nm²/kg²)
• M = Point mass (kg)
• r = Distance from centre (m)
• V = Gravitational potential (J/kg)
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31
Q

What kind of law is the equation that gives g relative to the distance from a point mass?

A

Inverse square law (since g is inversely proportional to r²)

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32
Q

Describe the graph of g against r for a point mass.

A
  • Does not cross y-axis
  • Curve starts at its highest point at a certain x-value (RE - radius of the Earth)
  • It then curves like a 1/x² graph and never quite reaches the x-axis
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33
Q

Remember to practise drawing out the graph of g against r for a point mass.

A

See diagram of 121 of revision guide.

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34
Q

What is gravitational potential?

A

The gravitational potential energy that a unit mass would have at that point in a gravitational field.

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35
Q

What is the symbol for gravitational potential?

A

V

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36
Q

What is the equation for gravitational field strength with F and M?

A

g = F/M

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37
Q

What are the units for gravitational potential?

A

J/kg

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38
Q

g= F/M, what is the F?

A

Force experienced by a mass in the field

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39
Q

What is the difference between gravitational potential energy and gravitational potential?

A
  • Gravitational potential -> GPE that a unit mass would have at a given point in a gravitational field
  • Gravitational potential energy -> The energy that a mass has due to its position in a gravitational field
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40
Q

Why do we assume g is constant

A

Almost uniform field near earth’s surface

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41
Q

What is the equation for gravitational potential?

A

V = -GM / r

Where:
• V = Gravitational potential (J/kg)
• G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
• M = Mass of point mass (kg)
• r = Distance from centre of point mass (m)

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42
Q

What is unusual about gravitational potential and GPE? Why?

A
  • They are negative, since you can think of it of as negative energy since work has to be done to move an object out of the field
  • They becomes less negative with distance from the point mass
  • At infinite distance, the gravitational potential is 0J/kg and GPE is 0J
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43
Q

Which quantities in gravitational field questions are always negative?

A
  • Gravitational potential

* Gravitational potential energy (GPE)

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44
Q

How is g = GM / r² derived?

A
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45
Q

Describe how gravitational potential (and GPE) changes with distance from a planet’s surface. (3)

A
  • Most negative on the planet’s surface
  • Becomes less negative with distance from the planet
  • 0J/kg at infinite distance
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46
Q

At infinite distance from a planet, what is the gravitational potential and GPE?

A
  • Gravitational potential (0J/kg)

* GPE (0J)

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47
Q

Describe a graph of V against r for the Earth.

A
  • Does not cross y-axis
  • Curve starts at its most negative point at a certain x-value (RE - radius of the Earth)
  • It then curves like a -1/x graph and never quite reaches the x-axis
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48
Q

Because Gravitational fields are vectors, what can you do to them?

A

add up to find combined effect of more than 1 object

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49
Q

How can you work out the value of g at a certain point using a V-r graph for a point mass?

A
  • Find the gradient at any point

* This is because g = -ΔV / Δr

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50
Q
A
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51
Q

Describe a graph of g against r for the Earth.

A
  • Does not cross y-axis
  • Curve starts at its highest point at a certain x-value (RE - radius of the Earth)
  • It then curves like a 1/x graph and never quite reaches the x-axis
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52
Q

How do you work out ΔV using a g-r graph?

A
  • Area under the curve between two x-values

* Because -ΔV = g x Δr

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53
Q

Remember to practise drawing out all 3 gravitational field graphs. Also, practise finding different quantities from them.

A

Pgs 121 + 122 of revision guide

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54
Q

What is escape velocity?

A
  • The velocity at which an object’s kinetic energy is equal to minus its gravitational potential energy
  • It is the minimum velocity at which an object must travel in order to escape a gravitational field
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55
Q

Why is potential negative?

A

Have to do work against the field to move an object out of it.

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56
Q

What is an object’s total energy when it travels at escape velocity?

A
  • Zero

* Because the kinetic energy and GPE sum to 0 (since GPE is always negative)

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57
Q

What is the equation for escape velocity?

A

v = √(2GM/r)

Where:
• v = Escape velocity (ms⁻²)
• G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
• M = Mass of point mass (kg)
• r = Distance from centre of point mass (m)

NOTE: Not given in exam.

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58
Q

Derive the equation for escape velocity.

A
  • KE = 1/2mv²
  • GPE = -GMm/r
  • 1/2mv² = GMm/r
  • 1/2v² = GM/r
  • v² = 2GM/r
  • v = √(2GM/r)
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59
Q

What is the equation for GPE relative to G, M and r instead of mgh?

A

GPE = -GMm/r

This is derived from V = -GM/r

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60
Q

How do you derive GPE = -GMm/r

A

Work done = m x V.

V = -GM/r

replace V with mV (which is work done) =
mV = -GMm/r, which is
GPE = -GMm/r

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61
Q

How do you find the change in kinetic energy of a satellite when it moves from and orbit of R1 to a lower orbit of R2?

A

(GPE lost = KE gained).

v = √(GM / r).

KE = 1/2 mv^2.

KE = 1/2 m(√(GM / r))^2

KE = GMm/2r

Change in KE = GMm/2(R1) - GMm/2(R2)

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62
Q

Is escape velocity dependent on the mass of the object?

A

No, it is the same for all masses in a gravitational field.

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63
Q

What is gravitational potential difference?

A

The energy needed to move a unit mass between two points in a grav field

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64
Q

What is the equation for the work done when moving an object through a gravitational potential difference?

A

ΔW = mΔV

Where:
• ΔW = Work fine (J)
• m = Mass (kg)
• ΔV = Gravitational potential difference (J/kg)

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65
Q

What are equipotentials?

A

Lines (in 2D) or surfaces (in 3D) that join all of the points with the same potential (V).

If you travel along an equipotential, your potential doesn’t change.

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66
Q

How much work is done when moving an object along an equipotential?

A

0J
Change in potential = 0
Change in work done = Mass x change in potential.

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67
Q

Describe the equipotential around a uniform spherical mass.

A

Spherical surfaces

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68
Q

Describe how equipotential and field lines are related in gravitational fields.

A

They are perpendicular.

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69
Q

What force keeps an object undergoing circular motion in orbit?

A

Centripetal force

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70
Q

In the case of a satellite orbiting the Earth, what is the centripetal force?

A

Gravitational force.

They are kept in orbit by the gravitational “pull” of of the mass (Earth) they orbit.

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71
Q

Give the relationship between the time period and radius of an orbit.

A

• T² = 4π²r³ / GM
So
• T² ∝ r³

(NOTE: Not given in exam)

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72
Q

Derive the relationship between the period and radius of an orbit.

A

Find two equations with force and velocity and find velocity, v.
Then use the time period equation to change v into T:

• Centripetal force:
F = mv² / r
• Attraction due to gravity:
F = GMm / r² 
• mv² / r = GMm / r²
• v² = GMmr / r²m
• v = √(GM / r)
• Since one orbit is 2πr:
v = 2πr / T
• T = 2πr / v
• T = 2πr / √(GM / r)
• T = 2πr√r / √(GM)
• T² = 4π²r³ / GM
• Therefore:
T² ∝ r³
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73
Q

How is the speed of a satellite related to its orbital radius?

A

• v = √(GM / r)
So:
• v ∝ 1 / √r

So greater radius = lower speed

(NOTE: This comes from the first part of the T² ∝ r³ derivation.)

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74
Q

Remember to practise deriving the relationship between T and r for a satellite.

A

Pg 124 of revision guide

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75
Q

If T² ∝ r³, what can be said to be constant?

A

T² / r³ = Constant

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76
Q
A
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77
Q

What can be said about the energy of an orbiting satellite?

A

It is constant, since the kinetic and potential energy always sum to a constant value.

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78
Q

How can this equation: ΔW = mΔV, be used for potential energy, then how can you make it become: GPE = -GMm/r ?

A
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79
Q

Why is a satellite’s energy constant in circular orbit? (3)

A
  • Speed and distance above the Earth do not change
  • So the kinetic energy and potential energy are constant
  • So the total energy is always constant
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80
Q

Why is a satellite’s energy constant in elliptical orbit?

A
  • The satellite speeds up as it’s orbital radius decreases and slows down as orbital radius increases
  • So kinetic energy increases as potential energy decreases (and vice versa)
  • So the total energy remains constant
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81
Q

What is it important to remember about r?

A

It is measured from the centre of the orbit (or the centre of the point mass), not the surface of the Earth.

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82
Q

What is a synchronous orbit?

A

Where the orbital period = the rotational period of the orbited object.

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83
Q

What are the two types of satellite?

A
  • Geostationary

* Low orbit

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84
Q

What are geostationary satellites?

A

Satellites that have the same angular speed as the Earth turns below them, so that they stay in the same position above the Earth.

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85
Q

Describe the orbit that geostationary satellites have.

A

Synchronous, along the equator.

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86
Q

What is the time period of orbit of a geostationary satellite?

A

1 day

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87
Q

What is the orbital radius of a geostationary satellite?

A

42,000km (about 36,000km above the Earth’s surface)

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88
Q

What are geostationary satellites used for?

A

Sending TV and telephone signals.

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89
Q

What are low orbit satellites?

A

Satellites that orbit between 180-2000km above the Earth, so that they do not stay in the same place relative to the Earth.

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90
Q

Describe the orbit that low-orbit satellites have.

A

Usually in a plane that includes the north and south pole.

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91
Q

Compare the advantages of low orbit satellites and geostationary satellites.

A

Low orbit
• Cheaper to launch
• Require less powerful transmitters since they are close to Earth
Geostationary
• Do not require multiple satellites to achieve constant reception in one area

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92
Q

How is T against r plotted?

A

Logarithmic scale:

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93
Q

At what height do low orbit satellites orbit?

A

180-2000km above the surface

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94
Q

What are low orbit satellites used for?

A
  • Communications -> Cheap to launch and do not require powerful transmitters, although many are required for constant coverage
  • Imaging and weather -> Due to being close enough to see surface in high detail
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95
Q

What type of satellite can be used to monitor the whole Earth and why?

A
  • Low orbit satellites

* Each orbit is over a different part of the Earth’s surface as the Earth rotates underneath

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96
Q

Where does a satellite orbit for an elliptical orbit?

A
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97
Q

What kind of satellite is the ISS?

A

Low orbiting

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98
Q

State 2 reasons why rockets launched from the Earth’s surface do not need to achieve escape velocity to reach their orbit?

A

They don’t need to escape gravitational field, only need to reach the orbit = less energy required.

Energy is added during the flight (with fuel) providing a continuous thrust.

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99
Q

Does any charged object have an electric field around it?

A

Yes

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100
Q

What is an electric field?

A

A region where charged objects will experience a non-contact force.

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101
Q

What is the unit for electric charge?

A

Coulombs (C)

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102
Q

What is the symbol for electric charge?

A

Q

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103
Q

Can charge be positive and negative?

A

Yes

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104
Q

Oppositely charged particles…

A

Attract

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105
Q

Like charges…

A

Repel

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106
Q

What happens when a charged object is placed in an electric field?

A

It experiences a force.

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107
Q

In electric field questions, what can he assumed about a charged object that is a sphere?

A

All of its charge is at its centre.

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108
Q

How can electric fields be represented?

A

Using field lines.

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109
Q

State Coulomb’s law.

A
  • The magnitude of the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
  • F = 1/4πε₀ x Q₁Q₂/r²
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110
Q

Give the equation for Coulomb’s law.

A

F = 1/4πε₀ x Q₁Q₂/r²

Where:
• F = Force (N)
• ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
• Q = Charge (C)
• r = Distance between charges (m)
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111
Q

What type of law is Coulomb’s law?

A
  • Inverse square law

* Since F ∝ 1/r²

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112
Q

What is the significance of the ε in Coulomb’s law?

A
  • This is the permittivity of the material the charges are in
  • This affects the size of the force between the charges
  • If the system is in air, it can be considered the same as in a vacuum
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113
Q

What is electric field strength?

A

The force per unit positive charge exerted at a certain point in an electric field.

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114
Q

What is the symbol for electric field strength?

A

E

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115
Q

What is the unit for electric field strength?

A

N/C

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116
Q

What is the equation than defines electric field strength?

A

E = F/Q

Where:
• E = Electric Field Strength (N/C)
• F = Force (N)
• Q = Charge (C)

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117
Q

Is electric field strength a scalar or vector quantity?

A

Vector

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118
Q

Is electric field strength a constant?

A

No, it depends on where you are in the electric field (unless it is uniform).

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119
Q

What type of electric field does a point charge have?

A

Radial field

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120
Q

For 2 positive parallel plates, which way do the field lines point?

A

From the plate with more positive voltage to the plate with less positive voltage.

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121
Q

How can you measure electric field lines?

A
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122
Q

What does a field line diagram look like?

A
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123
Q

Give the equation for the electric field strength around a point charge.

A

E = 1/4πε₀ x Q/r²

Where:
• E = Electric field strength (N/C)
• ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
• Q = Charge of point charge
• r = Distance from the point charge
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124
Q

What type of equation is the equation that is used to find the electric field strength around a point charge?

A
  • Inverse square law

* Since E ∝ 1/r²

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125
Q

What happens to the field lines as you get further away from a point charge?

A

They get further apart.

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126
Q

Describe the graph for E against r for an electric field around a point charge.

A

1/x² graph.

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127
Q

When will a charged not follow the inverse square law?

A

If it isn’t a point charge (e.g. a metal sphere)

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128
Q

How can a uniform electric field be produced?

A

Connecting two parallel plates to opposite poles of a battery.

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129
Q

What can be said about electric field strength in a uniform electric field?

A

It is the same at all points.

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130
Q

What is the equation that defines electric field strength in a uniform electric field?

A

E = V/d

Where:
• E = Electric field strength (N/C or V/m)
• V = Potential difference (change) between plates (V)
• d = Distance between plates (m)

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131
Q

What is an alternative unit for electric field strength in a uniform field?

A

V/m

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132
Q

What can a uniform electric field be used for? How?

A
  • Determining whether a particle is charged.
  • If a particle curves in the same direction as the field lines, it is positively charged
  • If a particle curves in the opposite direction as the field lines, it is negatively charged
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133
Q

What angle will a charged particle that enters an electric field feel a constant force parallel to the electric field lines?

A

enters the field at right angles

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134
Q

What is a particle’s curved path in an electric field called?

A

Parabola

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135
Q

What is absolute electric potential?

A

The electric potential energy that a unit positive charge would have at a point in an electric field.

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136
Q

What effects electric potential?

A

Size of charge creating the electric field and distance from the charge.

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137
Q

What is the symbol for electric potential?

A

V

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138
Q

What are the units for electric potential?

A

Volts (V)

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139
Q

Give the equation for electric potential around a point charge.

A

V = 1/4πε₀ x Q/r

Where:
• V = Electric potential (V)
• ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
• Q = Charge of point charge
• r = Distance from the point charge
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140
Q

When is V positive around a point charge?

A

When Q is positive. Force is repulsive

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141
Q

When is V negative around a point charge?

A

When Q is negative. Force is attractive

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142
Q

When is the magnitude of the electric potential around a point charge the greatest?

A

On the surface of the charge.

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143
Q

What is electric potential (V) equal to at infinite distance?

A

0V

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144
Q

Describe the graph of V against r around a point charge for a repulsive force.

A
  • 1/x² graph

* This is because a repulsive force must mean a positive point charge, so V is always positive.

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145
Q

Describe the graph of V against r around a point charge for an attractive force.

A
  • -1/x² graph

* This is because an attractive force must mean a negative point charge, so V is always negative.

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146
Q

What equation relates electric field strength with the change in electric potential around a point charge?

A

E = ΔV / Δr

Where:
• E = Electric field strength (N/C or V/m)
• ΔV = Electric potential difference (V)
• Δr = Change in distance from the charge (m)

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147
Q

How can electric field strength be found from a V-r graph around a point charge?

A
  • Gradient of tangent

* Because E = ΔV / Δr

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148
Q

How can potential difference between two points be found from an E-r graph around a point charge?

A
  • Area under graph between two points

* Because E = ΔV / Δr so ΔV = E x Δr

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149
Q

What is electric potential difference?

A

The energy needed to move a unit (positive(?)) charge between two points.

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150
Q

What equation gives the work required to move a charge through an electric potential difference?

A

ΔW = Q x ΔV

Where:
• ΔW = Work done (J)
• Q = Charge being moved (C)
• ΔV = Electric potential difference (V)

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151
Q

What is the symbol for electric potential difference?

A

ΔV

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152
Q

Derive the formula for work done in moving a charge through an electric potential difference.

A
  • E = F / Q = ΔV / d
  • Fd = QΔV
  • ΔW = QΔV
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153
Q

What is the equation for the work done to move a mass through a gravitational field?

A

ΔW = mΔV

Where:
• ΔW = Work done (J)
• m = Mass (kg)
• ΔV = Potential difference (ΔV)

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154
Q

Derive the equation for the work done to move a mass through a gravitational field.

A
  • g = -ΔV / Δr = F / m (since the gravitational field is considered near uniform near the Earth)
  • mΔV = -FΔr
  • ΔW = mΔV
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155
Q

What are equipotentials in electric fields?

A

Lines that show all points of equal potential in the electric field.

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156
Q

What shape are equipotentials around a point charge?

A

Spherical

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157
Q

Describe what equipotentials look like between parallels plates (in a uniform electric field).

A

They are parallel to each plate, with equal spacing.

Right angles to field lines

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158
Q

What do equipotentials around a point charge and between two parallel plates look like?

A
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159
Q

What are the Inverse square laws that are seen in both electric and gravitational fields?

A
  • Force between two masses / point charges

* Field strength around a mass / point charge

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160
Q

Describe how the electric and gravitational field equations differ.

A
  • Q is used instead of m (or M)

* 1/4πε₀ is used instead of G

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161
Q

Remember to practise listing all the similarities between electric and gravitational fields.

A

Pg 130 of revision guide or pg 300 of revision guide

162
Q

What is the one important difference between electric and gravitational fields?

A

Gravitational fields are always attractive, whereas electric forces can be attractive or repulsive.

163
Q

At sub-atomic level, does electrostatic or gravitational force have a greater effect and why?

A
  • Electrostatic
  • Because the masses are tiny, so the gravitational force is also tiny
  • NOTE: There are other forces that keep the nucleus stable
164
Q

When can charge transfer between two objects?

A

When they slide past each other

165
Q

When two objects slide past each other, how is charge transferred?

A

Electrons leave one surface and join the other

166
Q

What is earthing?

A

When electrons move to or from the earth to balance charges on charged objects

167
Q

What happens, when charge is transferred between objects, if one of the objects is an insulator?

A

The charge can build up

168
Q

Why does charge build up on the dome of a Van de Graaf generator?

A

The dome is metal, but charge builds up as it is isolated

169
Q

What happens when a charged polythene rod is brought near to uncharged objects?

A

It attracts the object

170
Q

How do you get charge onto an electroscope?

A

∙ charged object e.g. polythene rod is brought near the metal plate

∙ gold leaf moves towards rod

∙ electroscope is earthed so charge is stored

171
Q

How can electric fields be represented?

A

Field lines

172
Q

What do field lines show?

A

The direction of the force that would be felt by a small positive charge

173
Q

What do equally spaced field lines show?

A

A uniform field

174
Q

What practical can be done to plot field lines?

A

Electrolytic tanks and conducting paper

∙ damp filter paper, potassium permanganate and 250V electrodes

∙ plot equipotential lines using a point probe attached to a voltmeter (field lines plotted perpendicular to equipotential line)

175
Q

What are the rules about field lines? (3)

A

∙ never start or stop in empty space

∙ never cross

∙ density of field lines shows strength of field

176
Q

Where do field lines stop and start?

A

Either on a charge or at infinity

177
Q

Why do field lines never cross?

A

If they did, a small positive charge place there would feel forces in different directions, which could be resolved into the one true direction of the field there

178
Q

What is a neutral point?

A

A point exactly between two like charges where no field exists

179
Q

What is the equation for electric field strength?

A

E = F / Q

180
Q

What is field strength?

A

The force per unit (positive) charge exerted by the field

181
Q

What are the units for electric field strength?

A

N C-1

182
Q

Summary of Coulomb’s law?

A

The force between two point charges is

∙ directly proportional to each of the charges Q1 and Q2

∙ inversely proportional to the square of their separation

183
Q

What is the equation for Coulomb’s law?

A

F = kQ1Q2 / r²

184
Q

What does k depend on in F=kQ1Q2 / r²?

A

The permittivity of the substance separating the charges

185
Q

What permittivity does every insulating material have?

A

Greater than the permittivity of free space

186
Q

What does it mean, in terms of charges, that the permittivity of water is about 80 times the permittivity of free space?

A

Makes the forces between charges 1/80th of value - when salt is put in water the forces are reduced and crystal structure collapses

187
Q

What equation do you get when the electric field and coulombs law equation are combined?

A

E = kQ / r²

188
Q

What does k equal in E = kQ / r²?

A

1 / 4πℇ

189
Q

How can the strength of the uniform field between parallel plates be made stronger?

A

∙ increase p.d. across plates

∙ moving plates closer together

190
Q

Equation for strength of a uniform field?

A

E = V / d

191
Q

What can electric field strength be measured in?

A

Vm-1 or NC-1

192
Q

Why can electric field strength be measured in Vm-1 or NC-1?

A

Work is done moving an object, and work is done when a charge moves through a p.d.

193
Q

How are electrons used in TVs, oscilloscopes and X-ray machines?

A

∙ electron gun produces electrons by thermionic emission

∙ then they are accelerated by an electric field

∙ as electrons accelerate across field, they lose potential energy but gain kinetic

(gain in Ek = loss in Ep)

194
Q

What happens in an electron deflection tube?

A

Moving electrons pass through an electric field between two plates

195
Q

What is the equation for the force on an electron in an electron beam, and why is this?

A

∙ F = e V / d

(as E=V/d and force on an electron charge is F=Ee

196
Q

What is the shape of the path when electron beams are deflected?

A

Curved, as the force (F=eV/d) is constant

197
Q

What is the difference between electric and gravitational fields, in terms of what ‘feels’ the force?

A

∙ electric - charge q

∙ gravitational - mass m

198
Q

What is the difference between electric and gravitational fields, in terms of their definition?

A

∙ electric - force per unit charge

∙ gravitational - force per unit mass

199
Q

What is the difference between electric and gravitational fields, in terms of their constant of proportionality?

A

Both inversely proportional to r²

200
Q

What is the difference between electric and gravitational fields, in terms of their force equation?

A

∙ electric - F=Eq

∙ gravitational - F=mg

201
Q

What is the difference between electric and gravitational fields, in terms of their direction of force?

A

∙ electric - like charges repel, unlike charges attract

∙ gravitational - all masses attract

202
Q

What is the difference between electric and gravitational fields, in terms of their relative strength?

A

∙ electric - strong at close range (responsible for chemical bonding)

∙ gravitational - weak except for massive bodies (responsible for motion of planets)

203
Q

Do all points in an electric field have an absolute electric potential?

A

Yes

204
Q

What is absolute electric potential?

A

The electric potential energy that a unit positive charge would have at that point

205
Q

What is absolute electric potential calculated using?

A

V = 1/4πℇ x Q/r

206
Q

What does r equal in V = 1/4πℇ x Q/r?

A

Distance from the charge Q

207
Q

What does the sign of electric potential depend on?

A

The sign of Q (V is +ve when Q is +ve and the force is repulsive)

208
Q

When will V (electric potential) be zero?

A

When r is

209
Q

For a V-r graph, what does the gradient of a tangent to the graph give?

A

The field strength at that point

210
Q

When will two points in an electric field have an electric potential difference between them?

A

If they have a different absolute electric potential

211
Q

What is electric potential difference?

A

The energy required to remove a unit charge between two points in an electric field that have a different electric potential

212
Q

How can electric potential difference be found?

A

Using the area under the graph of E against r

213
Q

Where are field lines in relation to equipotential lines?

A

Perpendicular

214
Q

What happens in terms of energy when you travel along an equipotential line?

A

No work is done so no energy is transferred

215
Q

For a charged sphere, where may charge considered to be?

A

At the centre

216
Q

When is electric potential zero?

A

At infinity

217
Q

What equation links V to E?

A

E = ΔV/Δr

218
Q

What is G?

A

The universal gravitational constant

219
Q

RATE THIS 5

A

hh

220
Q

What does the formula F = Gm1m2/r2 apply to?

A

Point masses, but spherical masses can be treated as point masses with all their mass concentrated in the centre

221
Q

Is the force in F = Gm1m2/r2 attractive or repulsive?

A

Always attractive

222
Q

What is a field?

A

A region of space around an object where other bodies feel a force due to it

223
Q

Is your pull on the earth the same as the earth’s pull on you?

A

Yes, but your gravitational field is far weaker

224
Q

What is gravitational field strength ?

A

The force per unit mass exerted at a given position in a gravitational field.

225
Q

If two objects of different masses are placed at the same point in a field will they experience the same field strength and gravitational force?

A

Will experience same field strength, but different gravitational forces

226
Q

When calculating gravitational field strength, what is the mass that matters?

A

The mass below you only

227
Q

Where does g = GM/r2 come from?

A

When objects are a distance from earth e.g. other planets

  • F = Gm1m2/r2
  • small mass m, and planet mass M - F = GMm/r2
  • but F=mg so mg = GMm/r2
  • therefore g = GM/r2
228
Q

What is Kepler’s third law?

A

The time of one orbit T, and the distance from the planet to the sun r, are related by T² ∝ r³

229
Q

How is T² ∝ r³ proven?

A
  • planet remains in orbit due to centripetal force (F=mv2/r)
  • F=Gm1m2/r2
  • GMm/r2 = mv2/r
  • but v = 2πr/T
  • so GM/r2 = 4π2r/T2
  • T2 = (4π2/GM) r3
230
Q

What are geostationary satellites used for?

A

Communications

231
Q

How many geostationary satellites would be able to cover the entire earth?

A

3 placed into orbit 120 degrees apart above the equator

232
Q

Why are the energy and costs required for launching a satellite into a geostationary orbit high?

A

Because they have to be launched so high

233
Q

Equation for GPE in a uniform field?

A

Change in GPE = mgh

234
Q

What is the value of GPE at infinite distance?

A

0

235
Q

What is GPE proportional to, in terms of r?

A

1/r

236
Q

What is the equation for GPE in a radial field?

A

GPE = –GMm/r

note this is not change in GPE

237
Q

When GPE = –GMm/r, what happens to GPE as you move closer to M?

A

GPE becomes more negative as at infinite distance GPE=0

238
Q

Why did someone come up with gravitational potential?

A

To get an expression involving energy which is independent of the mass placed in a field

239
Q

What are the two ways gravitational potential can be thought about?

A
  1. GP at a point in a field is the energy per unit mass (V=Ep/m so V=gh)
  2. GP is work done per unit mass in moving a small object from infinity to that point (ΔV=ΔE/m)
240
Q

Is gravitational potential a scalar or vector?

A

Scalar

241
Q

Is gravitational field strength vector or scalar?

A

Vector

242
Q

Is the force between two masses vector or scalar?

A

Vector

243
Q

Is gravitational potential energy vector or scalar?

A

Scalar

244
Q

What is the unit for gravitational potential?

A

J kg-1

245
Q

What do equipotentials do?

A

Join points of equal potential

246
Q

When V = -GM/r is used to calculate V at earth’s surface, V = -63 MJ kg-1. What does this mean?

A

63mJ of work needs to be done in order to move 1kg from the earth’s surface to infinity

247
Q

What type of graph is the graph of V against r?

A

A 1/r curve, not an inverse-square

248
Q

What is the derivation for the escape velocity equation?

A
  • Ep = -GMm/r and Ek=1/2mv²
  • energy is conserved so Ep+Ek=0
  • -GMm/r + 1/2mv² = 0
  • so v = √2GM/r
  • or √2gr as gr=GM/r
249
Q

What is a null point?

A

A point between two masses where the resultant g force is zero

250
Q

What are low earth orbits?

A
  • satellite systems used in telecommunications

* orbit between 400 and 1,000 miles above the earth’s surface

251
Q

What is a synchronous orbit?

A

An orbit where the satellite has a period equal to that of the body being orbited

252
Q

What is the radius of a geostationary orbit?

A

approx 42000km

253
Q

What do capacitors do?

A

Store electric charge

254
Q

Where are capacitors used?

A

In almost all electric circuits

255
Q

What does a capacitor consist of?

A

Two parallel metal plates separated by an insulator called a dielectric

256
Q

What is a dielectric?

A

The insulator in a capacitor that separates the two metal plates

257
Q

When will a capacitor have a greater capacitance?

A

When it can store more charge

258
Q

What is the capacitance of a capacitor?

A

The charge stored per unit of potential difference across it

259
Q

What is the equation for capacitance?

A

C = Q/V

260
Q

What is the unit of capacitance?

A

the farad, F

=1CV⁻¹

261
Q

Are farads large or small units?

A

Very large

262
Q

How are farads usually marked?

A

In pico or microfarads

1 pF = 10⁻¹²

263
Q

What may a capacitor have marked on it?

A

A working voltage which must not be exceeded

264
Q

Roughly, how much electric charge do capacitors store?

A

Small amounts, providing power for a short amount of time

265
Q

Why can charged capacitors be dangerous?

A

They can discharge all of their charge in a fraction of a second

266
Q

Where can capacitors be used?

A
  • camera flash
  • back up power supply
  • to smooth dc power supplies
267
Q

What happens in terms of electrons when a capacitor is charged?

A
  • electrons are pushed onto one plate and off the other
  • the power supply does work on the electrons so the Ep increases
  • this Ep is stored in the electric field between the plates
268
Q

In a V-Q graph, what is the area underneath the graph?

A

Energy stored

269
Q

Explain how a capacitor ‘gets’ charge.

A
  • during charging electrons flow from -ve terminal of power supply to one plate of capacitor and from other plate to +ve terminal
  • switch closed, charging starts, rate of flow of charge is large (i.e. big current) and this decreases with time and plates become more charged so resist further charging
270
Q

What happens, when charging a capacitor, to the rate of flow of charge?

A
  • at first rate of flow of charge/current is large

* this decreases with time as the plates become more charged so resisting any further charging

271
Q

What effect would adding a resistor in the circuit when charging a capacitor have?

A

Only affects time taken for capacitor to become fully charged and not the eventual p.d. across it

272
Q

What does the gradient of the tangent to the curve at a point on a Q-t graph give?

A

The current at that time

273
Q

How to find current at a particular time using a Q-t graph?

A

Gradient of tangent at a certain point

274
Q

On a current-time graph, what does the area underneath the curve give?

A

The charge stored

275
Q

What is T½ on a Q-t graph?

A

The time for the charging current to half

276
Q

What actually happens in a discharge circuit?

A
  • as soon as switch is closed, ‘large’ current flows and p.d. across capacitor drops
  • as charge flows from one plate to the other through the resistor the charge is neutralised and so the current falls
  • rate of decrease of p.d. also falls
277
Q

When is a capacitor fully discharged?

A

When the charge on the plates is zero and the current and p.d. are also zero

278
Q

How does a resistor affect the discharge of a capacitor?

A

The value of the resistor doesn’t affect the final p.d., only the time it takes to reach this value

279
Q

How does a larger resistor affect the time taken for a capacitor to discharge?

A

The bigger the resistor, the longer time taken to discharge

280
Q

What can a discharge curve apply to?

A

V, Q or I against time

281
Q

What is the area under the discharge curve of a I-t graph equal to?

A

The charge that has flowed

282
Q

What is the gradient of the tangent on a Q-t graph equal to?

A

The current at that point in time

283
Q

What is half life equal to?

A

0.69RC

284
Q

What is the time constant?

A

The time taken for the p.d. across the capacitor and the charge stored on the capacitor to drop to 1/e of their original values

285
Q

What is the gradient of the graphs of loge(current) etc. graphs?

A

All have same gradient; -1/RC

286
Q

What equation shows the factors affecting the capactiance of a parallel plate capacitor?

A

C = Aε0εr/d

287
Q

What does C equal in C = Aε0εr/d?

A

Capacitance (F)

288
Q

What does A equal in C = Aε0εr/d?

A

Cross sectional area of overlap of the plates (m²)

289
Q

What does ε0 equal in C = Aε0εr/d?

A

Permittivity of free space (Fm⁻¹)

290
Q

What does εr equal in C = Aε0εr/d?

A

Relative permittivity of the dielectric

291
Q

What does d equal in C = Aε0εr/d?

A

Distance between the plates (m)

292
Q

What is relative permittivity also known as in terms of capacitors?

A

The dielectric constant of the material

293
Q

What is εr calculated from?

A

εm / ε0

where εm is the permittivity of the material used as the dielectric

294
Q

What is the unit of εr?

A

No unit

295
Q

What is a dielectric material (dielectric for short)?

A

An electrical insulator that can be polarised by an applied electric field

296
Q

What happens when a dielectric is placed in an electric field?

A

Electric charges do not flow through the material as they do in a conductor, but only slightly shift from their average equilibrium positions causing dielectric polarisation

297
Q

When does dielectric polarisation occur?

A

When a dielectric is placed in an electric field and the electric charges shift from the average equilibrium positions

298
Q

What is the effect of dielectric polarisation?

A
  • +ve charges are displaced toward field and -ve shift in opposite direction
  • creates internal electric field that reduces overall field within dielectric so reducing p.d. across capacitor
299
Q

How is an internal electric field created in a capacitor?

A

The dielectric is placed in an electric field, dielectric polarisation occurs and creates an internal electric field

300
Q

What is the effect of an internal electric field in a dielectric?

A

It reduces the overall field within the dielectric itself, reducing the p.d. across the capacitor

301
Q

How can the p.d. return to its original value after dielectric polarisation?

A

Requires the addition of more charge onto the plates

302
Q

What effect does dielectric polarisation have on the capacitor overall?

A

The capacitor can store more charge for the same p.d. and increase its capacitance

303
Q

When will a wire in a magnetic field experience a force?

A

When it carries a current

304
Q

How can the direction of the force on a current carrying wire be worked out?

A

Using Fleming’s left hand rule

305
Q

What does each finger mean in Fleming’s left hand rule?

A

Thumb = Thrust/Force

First finger = field

Second finger = Current

306
Q

What equation is used to work out the magnitude of force on a current-carrying wire?

A

F = BIL

307
Q

What does F mean in F=BIL?

A

Force (N)

308
Q

What does B mean in F=BIL?

A

Flux Density (T)

309
Q

What does L mean in F=BIL?

A

Length of conductor in field (m)

310
Q

What does I mean in F=BIL?

A

Current (A)

311
Q

How is the tesla defined using words?

A

One newton per amp per metre

312
Q

How is the tesla defined using the equation?

A

1T = 1 N/Am

313
Q

How can the strength of a magnetic field be measured?

A

By the force per unit current per unit length acting on a current carrying conductor placed perpendicular to the lines of a uniform field

314
Q

How can magnetic flux density B be measured?

A

By the force per unit current per unit length acting on a current carrying conductor placed perpendicular to the lines of a uniform field

315
Q

What does the right hand thumb rule determine?

A

The direction of the magnetic field in a direction of current

316
Q

What directions are field and current relative to each other in F=BIL?

A

Perpendicular

317
Q

How is a wire with the current coming towards you drawn?

A

A circle with a dot in

318
Q

How is a wire with the current travelling away from you drawn?

A

A circle with a cross in like an arrow

319
Q

What happens to a charged particle when it moves through a magnetic field?

A

It experiences a force

320
Q

When a charged particle moves through a magnetic field and experiences a force, what is this force proportional to?

A
  • B - magnetic flux density
  • Q - charge on the particle
  • v - velocity of the particle
321
Q

When a charge is moving in a magnetic field, how can the force be calculated?

A

F = BQv

322
Q

What condition must be true when F=BQv is used to calculate the force on a charge?

A

The charge must be moving at 90° to the field

323
Q

In the equation F=BQv, what is the direction of the force given by?

A

Fleming’s left hand rule

324
Q

When a charged particle moves at right angles a magnetic field, what is the constant force perpendicular to?

A

Both the velocity and the field

325
Q

Why does the constant force on a particle in a magnetic field change the particle’s direction of motion and has no effect on speed?

A

The constant force is perpendicular to both the velocity and field

326
Q

Does the force from a magnetic field on a charged particle affect the particle’s speed?

A

No

327
Q

Does the force from a magnetic field on a charged particle affect the particle’s direction of motion?

A

Yes

328
Q

What is the result when a constant force acts on a charged particle in a magnetic field?

A

The particle travels in a circular path

329
Q

What does it mean for a charged particle in a magnetic field, that the constant force is perpendicular to the velocity and field?

A

The particle travels in a circular path

330
Q

How is the equation for the radius of the circular path which a charged particle follows derived?

A
  • BQv = mv²/r

* r = mv/BQ

331
Q

What is the equation for the radius of the circular path which a charged particle follows?

A

r = mv/BQ

332
Q

How is the equation for the time period for an electron in a magnetic field to make one rotation derived?

A
  • time = distance/speed
  • time = length of circular path/speed of electron or T=2πr/v
  • since r = mv/BQ, T = 2πmv/vBQ
  • T = 2πm/BQ
333
Q

Equation for time period of an electron in a magnetic field to make one rotation?

A

T = 2πm/BQ

334
Q

In a magnetic field of constant flux density, does the time period of an electron depend on its speed?

A

No

a faster moving electron moves in a circle of larger radius, but takes the same time to make one revolution

335
Q

Where might the circular path of charged particles in a magnetic field be applied?

A

Cyclotron

336
Q

What is magnetic flux given by?

A

Φ = BA

337
Q

What does Φ mean in Φ=BA?

A

Magnetic flux (Wb)

338
Q

What does A mean in Φ=BA?

A

Cross sectional area (m2)

339
Q

What does B mean in Φ=BA?

A

Flux density (T)

340
Q

What is magnetic flux measured in?

A

weber (Wb)

341
Q

What is 1 weber defined as?

A

1 Wb = 1T m2

342
Q

What happens to the equation Φ = BA if the plane of the area is not perpendicular to the field?

A

Φ = BAcosΘ

343
Q

What is flux linkage?

A

The magnetic flux linking the coil

344
Q

What is flux linkage given by?

A

Flux linkage = NΦ

345
Q

What does Faraday’s law state?

A

The magnitide of the induced emf is equal to the rate of change of flux linkage

346
Q

What does N mean in flux linkage = NΦ?

A

The number of turns in a coil i.e. the number of turns cutting the flux

347
Q

What is the equation relating to Faraday’s law (words)?

A

Induced emf = change in flux linkage/time taken

348
Q

What is the equation relating to Faraday’s law (symbols)?

A

E = ΔNΦ / Δt

349
Q

What does Faraday’s law essentially tell us?

A

The size of the induced emf

350
Q

How can we find the direction of the induced emf described in Faraday’s law?

A

Using Lenz’s law

351
Q

What is Lenz’s law

A

The direction of the induced emf is such that it will try to oppose the change in flux that is producing it

352
Q

Equation that relates to Lenz’s law?

A

E = - ΔNΦ / Δt

353
Q

What does the minus sign in Lenz’s law equation show?

A

That the emf is always induced in a direction so as to oppose the change in flux

354
Q

What does a generator do?

A

Converts kinetic energy to electical energy

355
Q

What do the slip rings in a generator do?

A

Rotate with the coil and press against stationary carbon brushes

356
Q

In a generator, which side of the coil makes contact with which brush?

A

Each side of the coil always makes contact with the same brush

357
Q

In a generator, what happens to flux linkage as the coil rotates at a steady rate?

A

The flux linkage constantly changes

358
Q

In a generator, how much a.c. does one revolution of the coil give?

A

One revolution of the coil gives one cycle of a.c.

359
Q

Overall, what increases the peak emf of a generator?

A

By increasing the rate of change of flux linkage of the coil as it spins

360
Q

How can the rate of change of flux linkage of the coil in a generator be increased, in order to increase peak emf?

A
  • using a coil with more turns
  • using a coil with a larger cross-sectional area
  • increasing the strength of the magnetic field
  • increasing the frequency of rotation of the coil
361
Q

What will the frequency of rotation of the coil affect in a generator?

A

The rate of change of flux linkage of the coil, as well as the frequency of the a.c. signal

362
Q

In a generator, what is the relationship between the frequency of rotation of the coil and the frequency of the ac signal?

A

They are directly proportional

363
Q

What are the equations for flux linkage when looking at generators?

A
  • flux linkage = BANcosΘ
  • flux linkage = BANcosωt
  • flux linkage = BANωsinωt
364
Q

In the equation flux linkage = BANcosΘ, what does Θ depend on? What equation does this result in?

A

The angular speed ω of the coil

giving flux linkage = BANcosωt

365
Q

What does ω stand for?

A

Angular speed in rad s-1

366
Q

How does induced emf in a generator vary? Why is this?

A

Sinusoidally, as max. change happens when Θ=90°

367
Q

What type of current do cells and batteries supply?

A

Direct

368
Q

What is a direct current?

A

Current flowing in one direction only

369
Q

What type of current does mains supply?

A

Alternating

370
Q

What is the peak value of ac current or pd?

A

The maximum in either direction

371
Q

How can peak value of ac be measured?

A

From the wave as the amplitude

372
Q

How is peak current denoted?

A

I₀

373
Q

How is peak voltage denoted?

A

V₀

374
Q

What is the peak to peak value of current or pd?

A

The range of values - the distance from the peak above the zero line to the peak below the zero line

375
Q

What is the time period of an ac current?

A

The time taken for one complete cycle/wave

376
Q

What is the root mean squared?

A

A value of current that produces the same heating effect in a resistor as the equivalent dc

377
Q

Why, for an ac current, is it impossible to assign a value to pd and current for a fixed value of time? What is done instead?

A

Current and pd is constantly changing so average would be zero

  • root mean squared produces same heating effect in a resistor as the equivalent dc
378
Q

What is an oscilloscope used for?

A

To show the sizes of voltages and currents in both dc and ac circuits

379
Q

What does a dc trace on an oscilloscope look like? Why?

A

A straight line, as the current is constant, so the voltage is constant

380
Q

What does an ac trace on an oscilloscope look like? Why?

A

A wave, as the current is constantly changing from maximum flow in one direction to maximum flow in the other direction, so voltage does the same

381
Q

What controls do we use on an oscilloscope?

A
  • volts/div dial

* time base dial

382
Q

What does the volts/div dial on an oscilloscope allow you to do?

A

Change how much each vertical square is worth

383
Q

What does the time base dial on an oscilloscope allow you to do?

A

Change how much each horizontal square is worth

384
Q

How can you measure the voltage of a dc supply using an oscilloscope?

A

Counting number of vertical squares from origin to line and multiply by volts/div

385
Q

How can the time for one period be measured using an oscilloscope?

A

Counting how many horizontal squares one wavelength is and multiply by time base

386
Q

What does a transformer do?

A

Changes the value of ac voltage

387
Q

What do transformers consist of?

A

Two coils wound around a soft iron core

388
Q

How does a transformer work?

A
  • ac current flows in the primary coil
  • producing a changing magnetic flux in the soft iron core
  • meaning the flux linkage of the secondary coil is constantly changing
  • and so an ac voltage is induced across it
389
Q

What does a step-up transformer do? Why is this?

A

Increases ac voltage, as secondary coil has more turns than primary coil

390
Q

What does a step-down transformer do? Why is this?

A

Decreases ac voltage, as secondary coil has fewer turns than primary coil

391
Q

In a transformer, what is the ratio of voltages equal to?

A

The ratio of turns

392
Q

What equation shows the ratio of voltages in transformers?

A

Vs / Vp = Ns/ Np

393
Q

What happens in terms of energy losses in an ideal transformer?

A

No energy is lost

394
Q

What is the equation for power in an ideal transformer, and under what condition?

A

VpIp = VsIs

provided no energy is lost

395
Q

What are eddy currents?

A

Looping currents induced by the changing magnetic flux in the core

396
Q

What do eddy currents do?

A

Create a magnetic field that acts against the field that induced them

397
Q

How do eddy currents dissipate energy?

A

By generating heat

398
Q

How can the energy loss from eddy currents be reduced?

A

By laminating the core

399
Q

How can the efficiency of a transformer be calculated?

A

Ratio of power out to power in:

E = IsVs / IpVp

400
Q

What is voltage stepped up to through the National Grid?

A

400 000 V

Physics (43 decks)

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