Gravitational and Electric Fields

Question 1

What is a force field?

Answer 1

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

Question 2

What is a gravitational field?

Answer 2

A gravitational field is a region surrounding a mass in which any other object with mass will experience an attractive, non-contact force.

Question 3

What are gravitational field lines?

Answer 3

Gravitational field lines are arrows showing the direction of force that masses would feel in a gravitational field.

Question 4

What is Newton’s Law of Gravitation?

Answer 4

F = Gm1m2 / r^2

Shows that F in inversely proportional to r^2.

Question 5

How is Newton’s Law of Gravitation an inverse square law?

Answer 5

F= Gm1m2 / r^2

G is a constant, so F ∝ 1/r^2

Question 6

What are the rules of drawing gravitational field lines?

Answer 6

1. Always point towards the centre of the mass producing the field
2. Show the direction that the mass would move if placed in the field
3. Are closer together where the field is stronger
4. Are further apart where the field is weaker
5. Never cross over each other

Question 7

What is the gravitational field strength?

Answer 7

The gravitational field strength, g, is equal to the force per unit mass.

g = F/m given in exam

Question 8

What is the gravitational potential?

Answer 8

The gravitational potential, V, is the gravitational potential energy that a unit mass at that point would have.

V = -GM/r given in exam

Question 9

Why is gravitational potential energy negative?

Answer 9

Gravitational potential is defined as zero at infinity.

Work has to be done to move an object out of a gravitational field - and this is a gain of energy.

Gravitational potential is the most negative on the surface of the mass creating the field.

Question 10

What are equipotentials?

Answer 10

​An equipotential is a surface of constant potential.

No work is done by the field when an object moves along an equipotential.

This is the same for gravitational fields and electric fields.

Question 11

What is Kepler’s Third Law?

Answer 11

T^3 ∝ r^3 for an object in orbit

Question 12

What is a synchronous orbit?

Answer 12

A Synchronous orbit is an orbit that has an orbital period equal to the rotational period of the orbited object.

E.g., a satellite on Earth with a time period of one day.

Question 13

What is a geostationary orbit?

Answer 13

Geostationary orbits are a type of synchronous orbit that are always above the same point on Earth.

To do this, they must always be directly above the equator.

Their orbit takes exactly one day.

Question 14

What is a low orbit?

Answer 14

Low orbits orbit at heights between 180-2000km above Earth.

Question 15

What is escape velocity?

Answer 15

Escape velocity is the ​minimum velocity it must travel at in order to escape the gravitational field at the surface of a mass​.

This is the velocity at which the object’s ​kinetic energy is equal to the magnitude of its gravitational potential energy​.

v =√(2GM/r) not given in exam

Question 16

Where does the equation for escape velocity,

v =√(2GM/r) , come from?

Answer 16

Escape velocity: kinetic energy is equal to the gravitational potential energy​.

Ek = Ep

1/2 mv^2 = GMm/r

v = √(2GM/r)

Question 17

What is the gravitational potential difference?

Answer 17

The ​gravitational potential difference​ is the ​energy needed to move a unit mass between two points.

Work done = mΔV given in exam

Question 18

State how Kepler’s Third Law is derived.

Answer 18

Kepler’s Third Law for objects in orbit:

1. Force acting on object in circular motion - centripetal force.
2. Equate force due to gravity and centripetal force.
3. Solve for v.
4. Find time period in terms of v and circumference.
5. Substitute previous value for v in equation for time period.
6. Square both sides.

Question 19

What is an electric field?

Answer 19

An electric field is a region surrounding a charged object which causes a force to be exerted on any charged object placed within the field.

Question 20

What is electric field strength?

Answer 20

Electric field strength, E, is ​the force per unit positive charge exerted on a charged object placed at that point in the field.

E is a vector pointing in the direction that a positive charge would move.

E = F/Q given in exam

Question 21

What is Coulomb’s Law?

Answer 21

Coulomb’s Law is:

F = 1/4πε0 x Q1Q2/r^2

Question 22

What are the two implications of Coulomb’s Law?

Answer 22

F = 1/4πε0 x Q1Q2/r^2

This suggests that:

1. The force between two point charges is directly proportional to the product of their charges
2. The force between two point charges in inversely proportional the the square of the distance between them

Question 23

What is a uniform electric field?

Answer 23

A uniform electric field can be produced by connecting two parallel plates to the opposite poles of a battery.

The field strength, E, is the same at all points between the two plates.

E = V/d given in exam

Question 24

How can a uniform electric field be used to determine if a particle is charged or not?

Answer 24

If a charged particle is travelling in a uniform electric field, its path will bend.

Since field lines show the direction a POSITIVE point charge would take, positive charges bend towards the field lines and negative charges bend away from the field lines.

Question 25

What is electric potential?

Answer 25

Electric potential is the work done per unit charge on a positive test charge in bringing it from infinity to that point in the field.

Question 26

What does the sign of V, electric potential, depend on?

Answer 26

V = 1/4πε0 x Q/r

So the sign of V depends on the charge Q.

If Q is positive, then V is also positive, because the force is repulsive.
(Charge is positive and point charge assumed positive)

If Q is negative, then V is also negative, because the force is attractive.
(Charge is negative and point charge assumed positive)

Question 27

Describe what a graph would look like for V against r with a repulsive force.

Answer 27

For a graph of V against r with a repulsive force:

V is initially positive and tends to zero as r increases towards infinity.

Question 28

Describe what a graph would look like for V against r with an attractive force.

Answer 28

For a graph of V against r with an attractive force:

V is initially negative and tends to zero as r increases towards infinity.

Question 29

How do you derive the equation for work done,

ΔW = QΔV?

Answer 29

Imagine two parallel plates with a potential difference of ΔV across them - creating a uniform electric field.

1. We know that EFS is given by E = F/Q = ΔV/d
2. Rearrange to give Fd = QΔV
3. Work done = force x distance moved
4. Therefore, ΔW = QΔV

Question 30

How would you find the electric field strength from a graph of V against r?

Answer 30

Make a tangent at a point and find the gradient - this will give the electric field strength at that point.

E = ΔV/Δr given in exam

Question 31

What is the main difference between gravitational fields and electric fields?

Answer 31

Gravitational forces are always attractive.

Electric forces can be attractive or repulsive.