A charged sphere in a gravitational field is initially stationary between two parallel metal plates. There is a potential difference V between the plates.

Three changes can be made:

I.   Increase the separation of the metal plates
II.  Increase V
III. Apply a magnetic field into the plane of the paper

What changes made separately will cause the charged sphere to accelerate?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

Show that V = –g(R + h).

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

An object of mass $m$ released from rest near the surface of a planet has an initial acceleration $z$. What is the gravitational field strength near the surface of the planet?

A.  $z$

B.  $\frac{z}{m}$

C.  $mz$

D.  $\frac{m}{z}$

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.