Section 9 - Gravitational and Electric Fields Flashcards
What is a force field?
A region where an object will experience a non-contact force.
What do force fields cause?
Interactions between objects or particles.
What is a gravitational field?
A region where objects with mass will experience an attractive force.
How can a force field be represented?
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.
How are field lines used to show the strength of a field?
The further apart the lines are, the weaker the field.
Describe the gravitational field of the Earth.
- 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
What does Earths radial field look like?
What will the force experienced by an object in a gravitational field always be?
Attractive
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
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)
Where do we assume all the weight is concentrated for objects that experience a force?
In the centre - e.g. uniform spheres
When talking about a mass of an object in orbit, what is M and what is m
M = mass of larger object m = mass of smaller, orbiting object
How do you get the equation for speed of an object orbiting a larger object (e.g. a planet)? not found on data sheet
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
What is the equation of the time period of earths orbit?
Time = distance/speed.
T = 2πr/v
What type of law is Newton’s Law of Gravitation and how can this be symbolised?
- Inverse square law
* F ∝ 1 / r²
If the distance between 2 point masses is doubled, what happens to the magnitude of the gravitational force between them?
It is one quarter of the original.
What has a bigger impact on the size of the gravitational force, the distance between them or the mass?
- The distance
* This can be seen with Newton’s Law of Gravitation
In gravitational calculations, what is G?
- The gravitational constant
- It is used in some equations
- 6.67 x 10^-11 Nm²/kg²
What is gravitational field strength?
• The force per unit mass exerted at a given position in a gravitational field.
OR
• The acceleration of a mass in a gravitational field.
What is the symbol for gravitational field strength?
g
What are the units for gravitational field strength?
N/kg or m/s²
What is the equation that defines gravitational field strength?
g = F / m
Where:
• g = Gravitational field strength (N/kg)
• F = Force (N)
• m = Mass (kg)
Is the value of g constant throughout a field?
No, its value depends on the where you are in the field.
What is the value of g at the Earth’s surface?
9.81 N/kg (or m/s²)
Because F is a vector, where is the direction of the force always towards? (common sense)
Towards the the centre of the mass which caused the gravitational force
Is g constant around the world?
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.
The force on M1 due to M2 to equal and opposite to the force on…
M2 due to M1
In a radial field, how does g vary with the radius from the centre of the mass?
g is inversely proportional to r²
When we (humans) fall to the ground, why don’t we notice Earth’s acceleration towards us?
Describe the gravitational field around a point mass.
Radial
Give the equation for g around a point mass.
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)
What kind of law is the equation that gives g relative to the distance from a point mass?
Inverse square law (since g is inversely proportional to r²)
Describe the graph of g against r for a point mass.
- 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
Remember to practise drawing out the graph of g against r for a point mass.
See diagram of 121 of revision guide.
What is gravitational potential?
The gravitational potential energy that a unit mass would have at that point in a gravitational field.
What is the symbol for gravitational potential?
V
What is the equation for gravitational field strength with F and M?
g = F/M
What are the units for gravitational potential?
J/kg
g= F/M, what is the F?
Force experienced by a mass in the field
What is the difference between gravitational potential energy and gravitational potential?
- 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
Why do we assume g is constant
Almost uniform field near earth’s surface
What is the equation for gravitational potential?
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)
What is unusual about gravitational potential and GPE? Why?
- 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
Which quantities in gravitational field questions are always negative?
- Gravitational potential
* Gravitational potential energy (GPE)
How is g = GM / r² derived?
Describe how gravitational potential (and GPE) changes with distance from a planet’s surface.
- Most negative on the planet’s surface
- Becomes less negative with distance from the planet
- 0J/kg at infinite distance
At infinite distance from a planet, what is the gravitational potential and GPE?
- Gravitational potential (0J/kg)
* GPE (0J)
Describe a graph of V against r for the Earth.
- 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
Because Gravitational fields are vectors, what can you do to them?
add up to find combined effect of more than 1 object
How can you work out the value of g at a certain point using a V-r graph for a point mass?
- Find the gradient at any point
* This is because g = -ΔV / Δr
Describe a graph of g against r for the Earth.
- 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
How do you work out ΔV using a g-r graph?
- Area under the curve between two x-values
* Because -ΔV = g x Δr
Remember to practise drawing out all 3 gravitational field graphs. Also, practise finding different quantities from them.
Pgs 121 + 122 of revision guide
What is escape velocity?
- 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
Why is potential negative?
Have to do work against the field to move an object out of it.
What is an object’s total energy when it travels at escape velocity?
- Zero
* Because the kinetic energy and GPE sum to 0 (since GPE is always negative)
What is the equation for escape velocity?
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.
Derive the equation for escape velocity.
- KE = 1/2mv²
- GPE = -GMm/r
- 1/2mv² = GMm/r
- 1/2v² = GM/r
- v² = 2GM/r
- v = √(2GM/r)
What is the equation for GPE relative to G, M and r instead of mgh?
GPE = -GMm/r
This is derived from V = -GM/r
How do you derive GPE = -GMm/r
Work done = m x V.
V = -GM/r
replace V with mV (which is work done) =
mV = -GMm/r, which is
GPE = -GMm/r
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?
(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)
Is escape velocity dependent on the mass of the object?
No, it is the same for all masses in a gravitational field.
What is gravitational potential difference?
The energy needed to move a unit mass between two gravity sonar potentials.
What is the equation for the work done when moving an object through a gravitational potential difference?
ΔW = mΔV
Where:
• ΔW = Work fine (J)
• m = Mass (kg)
• ΔV = Gravitational potential difference (J/kg)
What are equipotentials?
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.
How much work is done when moving an object along an equipotential?
0J
Change in potential = 0
Change in work done = Mass x change in potential.
Describe the equipotential around a uniform spherical mass.
Spherical surfaces
Describe how equipotential and field lines are related in gravitational fields.
They are perpendicular.
What force keeps an object undergoing circular motion in orbit?
Centripetal force
In the case of a satellite orbiting the Earth, what is the centripetal force?
Gravitational force.
They are kept in orbit by the gravitational “pull” of of the mass (Earth) they orbit.
Give the relationship between the time period and radius of an orbit.
• T² = 4π²r³ / GM
So
• T² ∝ r³
(NOTE: Not given in exam)
Derive the relationship between the period and radius of an orbit.
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
How is the speed of a satellite related to its orbital radius?
• v = √(GM / r)
So:
• v ∝ 1 / √r
So greater radius = lower speed
(NOTE: This comes from the first part of the T² ∝ r³ derivation.)
Remember to practise deriving the relationship between T and r for a satellite.
Pg 124 of revision guide
If T² ∝ r³, what can be said to be constant?
T² / r³ = Constant
What can be said about the energy of an orbiting satellite?
It is constant, since the kinetic and potential energy always sum to a constant value.
How can this equation: ΔW = mΔV, be used for potential energy, then how can you make it become: GPE = -GMm/r ?
Why is a satellite’s energy constant in circular orbit?
- 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
Why is a satellite’s energy constant in elliptical orbit?
- 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
What is it important to remember about r?
It is measured from the centre of the orbit (or the centre of the point mass), not the surface of the Earth.
What is a synchronous orbit?
Where the orbital period is the same as the rotational period of the orbited object.
What are the two types of satellite?
- Geostationary
* Low orbit
What are geostationary satellites?
Satellites that have the same angular speed as the Earth turns below them, so that they stay in the same position above the Earth.
Describe the orbit that geostationary satellites have.
Synchronous, along the equator.
What is the time period of orbit of a geostationary satellite?
1 day
What is the orbital radius of a geostationary satellite?
42,000km (about 36,000km above the Earth’s surface)
What are geostationary satellites used for?
Sending TV and telephone signals.
What are low orbit satellites?
Satellites that orbit between 180-2000km above the Earth, so that they do not stay in the same place relative to the Earth.
Describe the orbit that low-orbit satellites have.
Usually in a plane that includes the north and south pole.
Compare the advantages of low orbit satellites and geostationary satellites.
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
How is T against r plotted?
Logarithmic scale:
At what height do low orbit satellites orbit?
180-2000km above the surface
What are low orbit satellites used for?
- 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
What type of satellite can be used to monitor the whole Earth and why?
- Low orbit satellites
* Each orbit is over a different part of the Earth’s surface as the Earth rotates underneath
Where does a satellite orbit for an elliptical orbit?
What kind of satellite is the ISS?
Low orbiting
State 2 reasons why rockets launched from the Earth’s surface do not need to achieve escape velocity to reach their orbit?
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.
Does any charged object have an electric field around it?
Yes
What is an electric field?
A region where charged objects will experience a non-contact force.
What is the unit for electric charge?
Coulombs (C)
What is the symbol for electric charge?
Q
Can charge be positive and negative?
Yes
Oppositely charged particles…
Attract
Like charges…
Repel
What happens when a charged object is placed in an electric field?
It experiences a force.
In electric field questions, what can he assumed about a charged object that is a sphere?
All of its charge is at its centre.
How can electric fields be represented?
Using field lines.
State Coulomb’s law.
- 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
Give the equation for Coulomb’s law.
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)
What type of law is Coulomb’s law?
- Inverse square law
* Since F ∝ 1/r²
What is the significance of the ε in Coulomb’s law?
- 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
What is electric field strength?
The force per unit positive charge exerted at a certain point in an electric field.
What is the symbol for electric field strength?
E
What is the unit for electric field strength?
N/C
What is the equation than defines electric field strength?
E = F/Q
Where:
• E = Electric Field Strength (N/C)
• F = Force (N)
• Q = Charge (C)
Is electric field strength a scalar or vector quantity?
Vector
Is electric field strength a constant?
No, it depends on where you are in the electric field (unless it is uniform).
What type of electric field does a point charge have?
Radial field
For 2 positive parallel plates, which way do the field lines point?
From the plate with more positive voltage to the plate with less positive voltage.
How can you measure electric field lines?
What does a field line diagram look like?
Give the equation for the electric field strength around a point charge.
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
What type of equation is the equation that is used to find the electric field strength around a point charge?
- Inverse square law
* Since E ∝ 1/r²
What happens to the field lines as you get further away from a point charge?
They get further apart.
Describe the graph for E against r for an electric field around a point charge.
1/x² graph.
When will a charged not follow the inverse square law?
If it isn’t a point charge (e.g. a metal sphere)
How can a uniform electric field be produced?
Connecting two parallel plates to opposite poles of a battery.
What can be said about electric field strength in a uniform electric field?
It is the same at all points.
What is the equation that defines electric field strength in a uniform electric field?
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)
What is an alternative unit for electric field strength in a uniform field?
V/m
What can a uniform electric field be used for? How?
- 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
What angle will a charged particle that enters an electric field feel a constant force parallel to the electric field lines?
enters the field at right angles
What is a particle’s curved path in an electric field called?
Parabola
What is absolute electric potential?
The electric potential energy that a unit positive charge would have at a point in an electric field.
What effects electric potential?
Size of charge creating the electric field and distance from the charge.
What is the symbol for electric potential?
V
What are the units for electric potential?
Volts (V)
Give the equation for electric potential around a point charge.
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
When is V positive around a point charge?
When Q is positive. Force is repulsive
When is V negative around a point charge?
When Q is negative. Force is attractive
When is the magnitude of the electric potential around a point charge the greatest?
On the surface of the charge.
What is electric potential (V) equal to at infinite distance?
0V
Describe the graph of V against r around a point charge for a repulsive force.
- 1/x² graph
* This is because a repulsive force must mean a positive point charge, so V is always positive.
Describe the graph of V against r around a point charge for an attractive force.
- -1/x² graph
* This is because an attractive force must mean a negative point charge, so V is always negative.
What equation relates electric field strength with the change in electric potential around a point charge?
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)
How can electric field strength be found from a V-r graph around a point charge?
- Gradient of tangent
* Because E = ΔV / Δr
How can potential difference between two points be found from an E-r graph around a point charge?
- Area under graph between two points
* Because E = ΔV / Δr so ΔV = E x Δr
What is electric potential difference?
The energy needed to move a unit (positive(?)) charge between two points.
What equation gives the work required to move a charge through an electric potential difference?
ΔW = Q x ΔV
Where:
• ΔW = Work done (J)
• Q = Charge being moved (C)
• ΔV = Electric potential difference (V)
What is the symbol for electric potential difference?
ΔV
Derive the formula for work done in moving a charge through an electric potential difference.
- E = F / Q = ΔV / d
- Fd = QΔV
- ΔW = QΔV
What is the equation for the work done to move a mass through a gravitational field?
ΔW = mΔV
Where:
• ΔW = Work done (J)
• m = Mass (kg)
• ΔV = Potential difference (ΔV)
Derive the equation for the work done to move a mass through a gravitational field.
- g = -ΔV / Δr = F / m (since the gravitational field is considered near uniform near the Earth)
- mΔV = -FΔr
- ΔW = mΔV
What are equipotentials in electric fields?
Lines that show all points of equal potential in the electric field.
What shape are equipotentials around a point charge?
Spherical
Describe what equipotentials look like between parallels plates (in a uniform electric field).
They are parallel to each plate, with equal spacing.
Right angles to field lines
What do equipotentials around a point charge and between two parallel plates look like?
What are the Inverse square laws that are seen in both electric and gravitational fields?
- Force between two masses / point charges
* Field strength around a mass / point charge
Describe how the electric and gravitational field equations differ.
- Q is used instead of m (or M)
* 1/4πε₀ is used instead of G
Remember to practise listing all the similarities between electric and gravitational fields.
Pg 130 of revision guide or pg 300 of revision guide
What is the one important difference between electric and gravitational fields?
Gravitational fields are always attractive, whereas electric forces can be attractive or repulsive.
At sub-atomic level, does electrostatic or gravitational force have a greater effect and why?
- Electrostatic
- Because the masses are tiny, so the gravitational force is also tiny
- NOTE: There are other forces that keep the nucleus stable
When can charge transfer between two objects?
When they slide past each other
When two objects slide past each other, how is charge transferred?
Electrons leave one surface and join the other
What is earthing?
When electrons move to or from the earth to balance charges on charged objects
What happens, when charge is transferred between objects, if one of the objects is an insulator?
The charge can build up
Why does charge build up on the dome of a Van de Graaf generator?
The dome is metal, but charge builds up as it is isolated
What happens when a charged polythene rod is brought near to uncharged objects?
It attracts the object
How do you get charge onto an electroscope?
∙ charged object e.g. polythene rod is brought near the metal plate
∙ gold leaf moves towards rod
∙ electroscope is earthed so charge is stored
How can electric fields be represented?
Field lines
What do field lines show?
The direction of the force that would be felt by a small positive charge
What do equally spaced field lines show?
A uniform field
What practical can be done to plot field lines?
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)
What are the rules about field lines?
∙ never start or stop in empty space
∙ never cross
∙ density of field lines shows strength of field
Where do field lines stop and start?
Either on a charge or at infinity
Why do field lines never cross?
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
What is a neutral point?
A point exactly between two like charges where no field exists
What is the equation for electric field strength?
E = F / Q
What is field strength?
The force per unit (positive) charge exerted by the field
What are the units for electric field strength?
N C-1
Summary of Coulomb’s law?
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
What is the equation for Coulomb’s law?
F = kQ1Q2 / r²
What does k depend on in F=kQ1Q2 / r²?
The permittivity of the substance separating the charges
What permittivity does every insulating material have?
Greater than the permittivity of free space
What does it mean, in terms of charges, that the permittivity of water is about 80 times the permittivity of free space?
Makes the forces between charges 1/80th of value - when salt is put in water the forces are reduced and crystal structure collapses
What equation do you get when the electric field and coulombs law equation are combined?
E = kQ / r²
What does k equal in E = kQ / r²?
1 / 4πℇ
How can the strength of the uniform field between parallel plates be made stronger?
∙ increase p.d. across plates
∙ moving plates closer together
Equation for strength of a uniform field?
E = V / d
What can electric field strength be measured in?
Vm-1 or NC-1
Why can electric field strength be measured in Vm-1 or NC-1?
Work is done moving an object, and work is done when a charge moves through a p.d.
How are electrons used in TVs, oscilloscopes and X-ray machines?
∙ 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)
What happens in an electron deflection tube?
Moving electrons pass through an electric field between two plates
What is the equation for the force on an electron in an electron beam, and why is this?
∙ F = e V / d
(as E=V/d and force on an electron charge is F=Ee
What is the shape of the path when electron beams are deflected?
Curved, as the force (F=eV/d) is constant
What is the difference between electric and gravitational fields, in terms of what ‘feels’ the force?
∙ electric - charge q
∙ gravitational - mass m
What is the difference between electric and gravitational fields, in terms of their definition?
∙ electric - force per unit charge
∙ gravitational - force per unit mass
What is the difference between electric and gravitational fields, in terms of their constant of proportionality?
Both inversely proportional to r²
What is the difference between electric and gravitational fields, in terms of their force equation?
∙ electric - F=Eq
∙ gravitational - F=mg
What is the difference between electric and gravitational fields, in terms of their direction of force?
∙ electric - like charges repel, unlike charges attract
∙ gravitational - all masses attract
What is the difference between electric and gravitational fields, in terms of their relative strength?
∙ electric - strong at close range (responsible for chemical bonding)
∙ gravitational - weak except for massive bodies (responsible for motion of planets)
Do all points in an electric field have an absolute electric potential?
Yes
What is absolute electric potential?
The electric potential energy that a unit positive charge would have at that point
What is absolute electric potential calculated using?
V = 1/4πℇ x Q/r
What does r equal in V = 1/4πℇ x Q/r?
Distance from the charge Q
What does the sign of electric potential depend on?
The sign of Q (V is +ve when Q is +ve and the force is repulsive)
When will V (electric potential) be zero?
When r is
For a V-r graph, what does the gradient of a tangent to the graph give?
The field strength at that point
When will two points in an electric field have an electric potential difference between them?
If they have a different absolute electric potential
What is electric potential difference?
The energy required to remove a unit charge between two points in an electric field that have a different electric potential
How can electric potential difference be found?
Using the area under the graph of E against r
Where are field lines in relation to equipotential lines?
Perpendicular
What happens in terms of energy when you travel along an equipotential line?
No work is done so no energy is transferred
For a charged sphere, where may charge considered to be?
At the centre
When is electric potential zero?
At infinity
What equation links V to E?
E = ΔV/Δr
What is G?
The universal gravitational constant
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What does the formula F = Gm1m2/r2 apply to?
Point masses, but spherical masses can be treated as point masses with all their mass concentrated in the centre
Is the force in F = Gm1m2/r2 attractive or repulsive?
Always attractive
What is a field?
A region of space around an object where other bodies feel a force due to it
Is your pull on the earth the same as the earth’s pull on you?
Yes, but your gravitational field is far weaker
What is gravitational field strength ?
A point in a body’s field as the gravitational force exerted on an object placed at that point, per kg of the object’s mass
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?
Will experience same field strength, but different gravitational forces
When calculating gravitational field strength, what is the mass that matters?
The mass below you only
Where does g = GM/r2 come from?
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
What is Kepler’s third law?
The time of one orbit T, and the distance from the planet to the sun r, are related by T² ∝ r³
How is T² ∝ r³ proven?
- 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
What are geostationary satellites used for?
Communications
How many geostationary satellites would be able to cover the entire earth?
3 placed into orbit 120 degrees apart above the equator
Why are the energy and costs required for launching a satellite into a geostationary orbit high?
Because they have to be launched so high
Equation for GPE in a uniform field?
Change in GPE = mgh
What is the value of GPE at infinite distance?
0
What is GPE proportional to, in terms of r?
1/r
What is the equation for GPE in a radial field?
GPE = –GMm/r
note this is not change in GPE
When GPE = –GMm/r, what happens to GPE as you move closer to M?
GPE becomes more negative as at infinite distance GPE=0
Why did someone come up with gravitational potential?
To get an expression involving energy which is independent of the mass placed in a field
What are the two ways gravitational potential can be thought about?
- GP at a point in a field is the energy per unit mass (V=Ep/m so V=gh)
- GP is work done per unit mass in moving a small object from infinity to that point (ΔV=ΔE/m)
Is gravitational potential a scalar or vector?
Scalar
Is gravitational field strength vector or scalar?
Vector
Is the force between two masses vector or scalar?
Vector
Is gravitational potential energy vector or scalar?
Scalar
What is the unit for gravitational potential?
J kg-1
What do equipotentials do?
Join points of equal potential
When V = -GM/r is used to calculate V at earth’s surface, V = -63 MJ kg-1. What does this mean?
63mJ of work needs to be done in order to move 1kg from the earth’s surface to infinity
What type of graph is the graph of V against r?
A 1/r curve, not an inverse-square
What is the derivation for the escape velocity equation?
- 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
What is a null point?
A point between two masses where the resultant g force is zero
What are low earth orbits?
- satellite systems used in telecommunications
* orbit between 400 and 1,000 miles above the earth’s surface
What is a synchronous orbit?
An orbit where the satellite has a period equal to that of the body being orbited
What is the radius of a geostationary orbit?
approx 42000km
What do capacitors do?
Store electric charge
Where are capacitors used?
In almost all electric circuits
What does a capacitor consist of?
Two parallel metal plates separated by an insulator called a dielectric
What is a dielectric?
The insulator in a capacitor that separates the two metal plates
When will a capacitor have a greater capacitance?
When it can store more charge
What is the capacitance of a capacitor?
The charge stored per unit of potential difference across it
What is the equation for capacitance?
C = Q/V
What is the unit of capacitance?
the farad, F
=1CV⁻¹
Are farads large or small units?
Very large
How are farads usually marked?
In pico or microfarads
1 pF = 10⁻¹²
What may a capacitor have marked on it?
A working voltage which must not be exceeded
Roughly, how much electric charge do capacitors store?
Small amounts, providing power for a short amount of time
Why can charged capacitors be dangerous?
They can discharge all of their charge in a fraction of a second
Where can capacitors be used?
- camera flash
- back up power supply
- to smooth dc power supplies
What happens in terms of electrons when a capacitor is charged?
- 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
In a V-Q graph, what is the area underneath the graph?
Energy stored
Explain how a capacitor ‘gets’ charge.
- 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
What happens, when charging a capacitor, to the rate of flow of charge?
- 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
What effect would adding a resistor in the circuit when charging a capacitor have?
Only affects time taken for capacitor to become fully charged and not the eventual p.d. across it
What does the gradient of the tangent to the curve at a point on a Q-t graph give?
The current at that time
How to find current at a particular time using a Q-t graph?
Gradient of tangent at a certain point
On a current-time graph, what does the area underneath the curve give?
The charge stored
What is T½ on a Q-t graph?
The time for the charging current to half
What actually happens in a discharge circuit?
- 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
When is a capacitor fully discharged?
When the charge on the plates is zero and the current and p.d. are also zero
How does a resistor affect the discharge of a capacitor?
The value of the resistor doesn’t affect the final p.d., only the time it takes to reach this value
How does a larger resistor affect the time taken for a capacitor to discharge?
The bigger the resistor, the longer time taken to discharge
What can a discharge curve apply to?
V, Q or I against time
What is the area under the discharge curve of a I-t graph equal to?
The charge that has flowed
What is the gradient of the tangent on a Q-t graph equal to?
The current at that point in time
What is half life equal to?
0.69RC
What is the time constant?
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
What is the gradient of the graphs of loge(current) etc. graphs?
All have same gradient; -1/RC
What equation shows the factors affecting the capactiance of a parallel plate capacitor?
C = Aε0εr/d
What does C equal in C = Aε0εr/d?
Capacitance (F)
What does A equal in C = Aε0εr/d?
Cross sectional area of overlap of the plates (m²)
What does ε0 equal in C = Aε0εr/d?
Permittivity of free space (Fm⁻¹)
What does εr equal in C = Aε0εr/d?
Relative permittivity of the dielectric
What does d equal in C = Aε0εr/d?
Distance between the plates (m)
What is relative permittivity also known as in terms of capacitors?
The dielectric constant of the material
What is εr calculated from?
εm / ε0
where εm is the permittivity of the material used as the dielectric
What is the unit of εr?
No unit
What is a dielectric material (dielectric for short)?
An electrical insulator that can be polarised by an applied electric field
What happens when a dielectric is placed in an electric field?
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
When does dielectric polarisation occur?
When a dielectric is placed in an electric field and the electric charges shift from the average equilibrium positions
What is the effect of dielectric polarisation?
- +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
How is an internal electric field created in a capacitor?
The dielectric is placed in an electric field, dielectric polarisation occurs and creates an internal electric field
What is the effect of an internal electric field in a dielectric?
It reduces the overall field within the dielectric itself, reducing the p.d. across the capacitor
How can the p.d. return to its original value after dielectric polarisation?
Requires the addition of more charge onto the plates
What effect does dielectric polarisation have on the capacitor overall?
The capacitor can store more charge for the same p.d. and increase its capacitance
When will a wire in a magnetic field experience a force?
When it carries a current
How can the direction of the force on a current carrying wire be worked out?
Using Fleming’s left hand rule
What does each finger mean in Fleming’s left hand rule?
Thumb = Thrust/Force
First finger = field
Second finger = Current
What equation is used to work out the magnitude of force on a current-carrying wire?
F = BIL
What does F mean in F=BIL?
Force (N)
What does B mean in F=BIL?
Flux Density (T)
What does L mean in F=BIL?
Length of conductor in field (m)
What does I mean in F=BIL?
Current (A)
How is the tesla defined using words?
One newton per amp per metre
How is the tesla defined using the equation?
1T = 1 N/Am
How can the strength of a magnetic field be measured?
By the force per unit current per unit length acting on a current carrying conductor placed perpendicular to the lines of a uniform field
How can magnetic flux density B be measured?
By the force per unit current per unit length acting on a current carrying conductor placed perpendicular to the lines of a uniform field
What does the right hand thumb rule determine?
The direction of the magnetic field in a direction of current
What directions are field and current relative to each other in F=BIL?
Perpendicular
How is a wire with the current coming towards you drawn?
A circle with a dot in
How is a wire with the current travelling away from you drawn?
A circle with a cross in like an arrow
What happens to a charged particle when it moves through a magnetic field?
It experiences a force
When a charged particle moves through a magnetic field and experiences a force, what is this force proportional to?
- B - magnetic flux density
- Q - charge on the particle
- v - velocity of the particle
When a charge is moving in a magnetic field, how can the force be calculated?
F = BQv
What condition must be true when F=BQv is used to calculate the force on a charge?
The charge must be moving at 90° to the field
In the equation F=BQv, what is the direction of the force given by?
Fleming’s left hand rule
When a charged particle moves at right angles a magnetic field, what is the constant force perpendicular to?
Both the velocity and the field
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?
The constant force is perpendicular to both the velocity and field
Does the force from a magnetic field on a charged particle affect the particle’s speed?
No
Does the force from a magnetic field on a charged particle affect the particle’s direction of motion?
Yes
What is the result when a constant force acts on a charged particle in a magnetic field?
The particle travels in a circular path
What does it mean for a charged particle in a magnetic field, that the constant force is perpendicular to the velocity and field?
The particle travels in a circular path
How is the equation for the radius of the circular path which a charged particle follows derived?
- BQv = mv²/r
* r = mv/BQ
What is the equation for the radius of the circular path which a charged particle follows?
r = mv/BQ
How is the equation for the time period for an electron in a magnetic field to make one rotation derived?
- 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
Equation for time period of an electron in a magnetic field to make one rotation?
T = 2πm/BQ
In a magnetic field of constant flux density, does the time period of an electron depend on its speed?
No
a faster moving electron moves in a circle of larger radius, but takes the same time to make one revolution
Where might the circular path of charged particles in a magnetic field be applied?
Cyclotron
What is magnetic flux given by?
Φ = BA
What does Φ mean in Φ=BA?
Magnetic flux (Wb)
What does A mean in Φ=BA?
Cross sectional area (m2)
What does B mean in Φ=BA?
Flux density (T)
What is magnetic flux measured in?
weber (Wb)
What is 1 weber defined as?
1 Wb = 1T m2
What happens to the equation Φ = BA if the plane of the area is not perpendicular to the field?
Φ = BAcosΘ
What is flux linkage?
The magnetic flux linking the coil
What is flux linkage given by?
Flux linkage = NΦ
What does Faraday’s law state?
The magnitide of the induced emf is equal to the rate of change of flux linkage
What does N mean in flux linkage = NΦ?
The number of turns in a coil i.e. the number of turns cutting the flux
What is the equation relating to Faraday’s law (words)?
Induced emf = change in flux linkage/time taken
What is the equation relating to Faraday’s law (symbols)?
E = ΔNΦ / Δt
What does Faraday’s law essentially tell us?
The size of the induced emf
How can we find the direction of the induced emf described in Faraday’s law?
Using Lenz’s law
What is Lenz’s law
The direction of the induced emf is such that it will try to oppose the change in flux that is producing it
Equation that relates to Lenz’s law?
E = - ΔNΦ / Δt
What does the minus sign in Lenz’s law equation show?
That the emf is always induced in a direction so as to oppose the change in flux
What does a generator do?
Converts kinetic energy to electical energy
What do the slip rings in a generator do?
Rotate with the coil and press against stationary carbon brushes
In a generator, which side of the coil makes contact with which brush?
Each side of the coil always makes contact with the same brush
In a generator, what happens to flux linkage as the coil rotates at a steady rate?
The flux linkage constantly changes
In a generator, how much a.c. does one revolution of the coil give?
One revolution of the coil gives one cycle of a.c.
Overall, what increases the peak emf of a generator?
By increasing the rate of change of flux linkage of the coil as it spins
How can the rate of change of flux linkage of the coil in a generator be increased, in order to increase peak emf?
- 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
What will the frequency of rotation of the coil affect in a generator?
The rate of change of flux linkage of the coil, as well as the frequency of the a.c. signal
In a generator, what is the relationship between the frequency of rotation of the coil and the frequency of the ac signal?
They are directly proportional
What are the equations for flux linkage when looking at generators?
- flux linkage = BANcosΘ
- flux linkage = BANcosωt
- flux linkage = BANωsinωt
In the equation flux linkage = BANcosΘ, what does Θ depend on? What equation does this result in?
The angular speed ω of the coil
giving flux linkage = BANcosωt
What does ω stand for?
Angular speed in rad s-1
How does induced emf in a generator vary? Why is this?
Sinusoidally, as max. change happens when Θ=90°
What type of current do cells and batteries supply?
Direct
What is a direct current?
Current flowing in one direction only
What type of current does mains supply?
Alternating
What is the peak value of ac current or pd?
The maximum in either direction
How can peak value of ac be measured?
From the wave as the amplitude
How is peak current denoted?
I₀
How is peak voltage denoted?
V₀
What is the peak to peak value of current or pd?
The range of values - the distance from the peak above the zero line to the peak below the zero line
What is the time period of an ac current?
The time taken for one complete cycle/wave
What is the root mean squared?
A value of current that produces the same heating effect in a resistor as the equivalent dc
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?
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
What is an oscilloscope used for?
To show the sizes of voltages and currents in both dc and ac circuits
What does a dc trace on an oscilloscope look like? Why?
A straight line, as the current is constant, so the voltage is constant
What does an ac trace on an oscilloscope look like? Why?
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
What controls do we use on an oscilloscope?
- volts/div dial
* time base dial
What does the volts/div dial on an oscilloscope allow you to do?
Change how much each vertical square is worth
What does the time base dial on an oscilloscope allow you to do?
Change how much each horizontal square is worth
How can you measure the voltage of a dc supply using an oscilloscope?
Counting number of vertical squares from origin to line and multiply by volts/div
How can the time for one period be measured using an oscilloscope?
Counting how many horizontal squares one wavelength is and multiply by time base
What does a transformer do?
Changes the value of ac voltage
What do transformers consist of?
Two coils wound around a soft iron core
How does a transformer work?
- 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
What does a step-up transformer do? Why is this?
Increases ac voltage, as secondary coil has more turns than primary coil
What does a step-down transformer do? Why is this?
Decreases ac voltage, as secondary coil has fewer turns than primary coil
In a transformer, what is the ratio of voltages equal to?
The ratio of turns
What equation shows the ratio of voltages in transformers?
Vs / Vp = Ns/ Np
What happens in terms of energy losses in an ideal transformer?
No energy is lost
What is the equation for power in an ideal transformer, and under what condition?
VpIp = VsIs
provided no energy is lost
What are eddy currents?
Looping currents induced by the changing magnetic flux in the core
What do eddy currents do?
Create a magnetic field that acts against the field that induced them
How do eddy currents dissipate energy?
By generating heat
How can the energy loss from eddy currents be reduced?
By laminating the core
How can the efficiency of a transformer be calculated?
Ratio of power out to power in:
E = IsVs / IpVp
What is voltage stepped up to through the National Grid?
400 000 V
