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aqa a-level 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 is Newton’s Law of Gravitation?

A
  • An equation used to calculate the gravitational force between two point masses
  • F = Gm₁m₂ / r²
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9
Q

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

A

Attractive

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10
Q

What is the equation for the gravitational force between two point masses (Newton’s Law of Gravitation)?

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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11
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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12
Q

When talking about a mass of an object in orbit, what is M (or M1) and what is m (or M2)

A 
M = mass of larger object
m = mass of smaller, orbiting object
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13
Q

How do you get the equation for speed of an object orbiting a larger object (e.g. a planet)?

A

GMm/r^2 = mv^2/r.

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

V = squareroot(GM/r)

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14
Q

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

A

Time = distance/speed.

T = 2πr/v

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15
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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16
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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17
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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18
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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19
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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20
Q

What is the symbol for gravitational field strength?

A

g

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21
Q

What are the units for gravitational field strength?

A

N/kg or m/s²

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22
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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23
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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24
Q

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

A

9.81 N/kg (or m/s²)

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25
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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26
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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27
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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28
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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29
Q

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

A
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30
Q

Describe the gravitational field around a point mass.

A

Radial

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31
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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32
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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33
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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34
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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35
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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36
Q

What is the symbol for gravitational potential?

A

V

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37
Q

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

A

g = F/M

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38
Q

What are the units for gravitational potential?

A

J/kg

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39
Q

g= F/M, what is the F?

A

Force experienced by a mass in the field

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40
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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41
Q

Why do we assume g is constant

A

Almost uniform field near earth’s surface

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42
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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43
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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44
Q

Which quantities in gravitational field questions are always negative?

A
  • Gravitational potential

* Gravitational potential energy (GPE)

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45
Q

How is g = GM / r² derived?

A
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46
Q

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

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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47
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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48
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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49
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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50
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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51
Q
A
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52
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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53
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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54
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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55
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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56
Q

Why is potential negative?

A

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

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57
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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58
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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59
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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60
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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61
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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62
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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63
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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64
Q

What is gravitational potential difference?

A

The energy needed to move a unit mass between two gravity sonar potentials.

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65
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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66
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.

67
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.

68
Q

Describe the equipotential around a uniform spherical mass.

A

Spherical surfaces

69
Q

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

A

They are perpendicular.

70
Q

What force keeps an object undergoing circular motion in orbit?

A

Centripetal force

71
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.

72
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)

73
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
74
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.)

75
Q

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

A

Pg 124 of revision guide

76
Q

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

A

T² / r³ = Constant

77
Q
A
78
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.

79
Q

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

A
80
Q

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

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
81
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
82
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.

83
Q

What is a synchronous orbit?

A

Where the orbital period is the same as the rotational period of the orbited object.

84
Q

What are the two types of satellite?

A
  • Geostationary

* Low orbit

85
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.

86
Q

Describe the orbit that geostationary satellites have.

A

Synchronous, along the equator.

87
Q

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

A

1 day

88
Q

What is the orbital radius of a geostationary satellite?

A

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

89
Q

What are geostationary satellites used for?

A

Sending TV and telephone signals.

90
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.

91
Q

Describe the orbit that low-orbit satellites have.

A

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

92
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

93
Q

How is T against r plotted?

A

Logarithmic scale:

94
Q

At what height do low orbit satellites orbit?

A

180-2000km above the surface

95
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
96
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

97
Q

Where does a satellite orbit for an elliptical orbit?

A
98
Q

What kind of satellite is the ISS?

A

Low orbiting

99
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.

100
Q

Does any charged object have an electric field around it?

A

Yes

101
Q

What is an electric field?

A

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

102
Q

What is the unit for electric charge?

A

Coulombs (C)

103
Q

What is the symbol for electric charge?

A

Q

104
Q

Can charge be positive and negative?

A

Yes

105
Q

Oppositely charged particles…

A

Attract

106
Q

Like charges…

A

Repel

107
Q

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

A

It experiences a force.

108
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.

109
Q

How can electric fields be represented?

A

Using field lines.

110
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
111
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)
112
Q

What type of law is Coulomb’s law?

A
  • Inverse square law

* Since F ∝ 1/r²

113
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
114
Q

What is electric field strength?

A

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

115
Q

What is the symbol for electric field strength?

A

E

116
Q

What is the unit for electric field strength?

A

N/C

117
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)

118
Q

Is electric field strength a scalar or vector quantity?

A

Vector

119
Q

Is electric field strength a constant?

A

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

120
Q

What type of electric field does a point charge have?

A

Radial field

121
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.

122
Q

How can you measure electric field lines?

A
123
Q

What does a field line diagram look like?

A
124
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
125
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

126
Q

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

A

They get further apart.

127
Q

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

A

1/x² graph.

128
Q

When will a charged not follow the inverse square law?

A

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

129
Q

How can a uniform electric field be produced?

A

Connecting two parallel plates to opposite poles of a battery.

130
Q

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

A

It is the same at all points.

131
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)

132
Q

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

A

V/m

133
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
134
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

135
Q

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

A

Parabola

136
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.

137
Q

What effects electric potential?

A

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

138
Q

What is the symbol for electric potential?

A

V

139
Q

What are the units for electric potential?

A

Volts (V)

140
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
141
Q

When is V positive around a point charge?

A

When Q is positive. Force is repulsive

142
Q

When is V negative around a point charge?

A

When Q is negative. Force is attractive

143
Q

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

A

On the surface of the charge.

144
Q

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

A

0V

145
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.

146
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.

147
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)

148
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

149
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

150
Q

What is electric potential difference?

A

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

151
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)

152
Q

What is the symbol for electric potential difference?

A

ΔV

153
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
154
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)

155
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
156
Q

What are equipotentials in electric fields?

A

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

157
Q

What shape are equipotentials around a point charge?

A

Spherical

158
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

159
Q

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

A
160
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

161
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

162
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

163
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.

164
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

aqa a-level physics (14 decks)

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