10.2 Fields at Work

A satellite of mass 2000 kg is in the Earth’s gravitational field. It moves radially from a point where the gravitational potential is –40 MJ kg^–1 to a point where the gravitational potential is –10 MJ kg^–1. What is the direction of movement of the satellite and the change in its gravitational potential energy?

Which graph shows how the kinetic energy E_K, the potential energy E_P and the total energy E of the international space station varies with distance x from the centre of Earth?

A probe is launched from the surface of the Earth, which has a radius R, at half the required escape velocity. 

What is the maximum height from the surface the probe will reach, before returning to the ground (with a bang)? 

The radius of the Sun is approximately 700 000 km. If all of its mass were compressed into a certain radius, it would collapse into a black hole, which is known to be a body from which "not even light can escape".

Which length gives the best estimate for the radius at which the Sun's mass would collapse into a black hole?

Use the following data: 

• Mass of the Sun = 2 × 10³⁰ kg
• Speed of light = 3 × 10⁸ m s^–1
• Gravitation constant = 6.67 × 10^–11 N m² kg^–2

The graph shows the variation of gravitational potential V with distance r from the centre of a spherical planet of mass M and radius R₀. 

Which statement best describes how to determine the gravitational field strength at a distance r = R from the planet?

The gravitational field strength is g and the gravitational potential is V at the surface of Earth, which has a radius of r.  

Which row in the table gives the correct value of the gravitational field strength and the gravitational potential at a height of 2r from Earth's surface? 

A particle of charge q is at point J in a uniform electric field of strength E. It is moved along a straight line joining point J to point K which is at an angle of Φ to the field lines, as shown in the diagram below. 

If the length of the path is JK, what is the change in electric potential energy of the charge q between J and K? 

Two positively charged particles, q₁ and q₂, are released from rest half-way between two oppositely charged parallel plates in a vacuum. The particles strike the negatively charged plate at the same time. 

Neglecting gravitational effects, which of the following statements is correct? 

Two charged parallel metal plates, X and Y, are separated by a distance of 2.0 m. X is charged to a potential of –180 V and Y is charged to a potential of +180 V. 

What is the magnitude and direction of the electric field strength at a point exactly mid-way between plates X and Y?