Coulomb's law

Two metal spheres each have radius r and charge Q. The force between them is F when the distance between their centres is x. Two other metal spheres each have radius and charge 2Q.

What is the force between these two spheres when the distance between their centres is x ?

Which is equal to ε₀?

The force between two point charges is F. The magnitude of each charge is doubled and the distance between them is halved.

What is the new force between the two charges?

the same distance?

Two protons are separated by a distance of 1 × 10⁻⁹ m.

Two point charges are separated by a distance of 200 mm. The force of attraction between them is 180 µN. The distance between the point charges is increased by 400 mm.

What is the new force of attraction?

An isolated solid conducting sphere is initially uncharged. Electrons are then transferred to the sphere.

State and explain the location of the excess electrons.

Figure 3 shows how the electric potential V varies with distance r from the centre of the sphere. The radius of the sphere is 0.10 m.

The magnitude of the electric field strength E is related to V by E =.

Determine, using this relationship, the magnitude of the electric field strength at a distance 0.30 m from the centre of the sphere.

State an appropriate SI unit for your answer.

The sphere acts as a capacitor because it stores charge at an electric potential.

Show that the capacitance of the sphere is approximately 1 × 10⁻¹¹ F.

Electrons leak away from the sphere with time and the amount of energy stored by the sphere decreases. At one instant, the magnitude of the electric potential of the sphere has fallen to 1.0 × 10⁶ V.

Calculate, for this instant, the change in the energy stored by the sphere.

Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion.

During the collapse of a supermassive star, helium-3 and oxygen-17 fuse to release energy. The equation for this reaction is

3 17 20

Table 2 gives data for these nuclei.

Calculate, in J, the energy released when this reaction occurs.

One model of nuclear fusion suggests that fusion happens when nuclei touch.

Initially the helium nucleus and oxygen nucleus are separated so that the force between them is negligible. They move towards each other until they fuse. Fusion occurs when their centres are separated by a distance of 5.1 × 10⁻¹⁵ m.

Figure 10 shows the initial positions and final positions of the nuclei.

Calculate the total change in electrostatic potential energy between the initial positions and final positions of the nuclei.

3He 34 S 17 O can undergo fusion reactions with either or at the same temperature 2 16 8 in a star.

The nucleus has properties that depend on its proton number and its nucleon number. These properties affect the fusion reaction.

34 3 Discuss, for this star, how these properties affect the rate of fusion of S with He 16 2 17 3 compared to the rate of fusion of 8 O with 2 He.

The diagram shows a particle with charge + Q and a particle with charge − Q separated by a distance d. The particles exert a force F on each other.

An additional charge of +2 Q is then given to each particle and their separation is increased to 2 d.

What is the force that now acts between the particles?

Two protons are separated by distance r. The electrostatic force between the two protons is X times the gravitational force between them.

What is the best estimate for X ?

Figure 11 shows alpha particles all travelling in the same direction at the same speed. The alpha particles are scattered by a gold (¹⁹⁷₇₉Au) nucleus. The path of alpha particle 1 is shown.

State the fundamental force involved when alpha particle 1 is scattered by the nucleus in Figure 11.

Draw an arrow at position X on Figure 11 to show the direction of the rate of change in momentum of alpha particle 1

Suggest one of the alpha particles in Figure 11 which may be deflected downwards with a scattering angle of 90°

Justify your answer.

Alpha particle 4 comes to rest at a distance of 5.5 × 10⁻¹⁴ m from the centre of the

Calculate the speed of alpha particle 4 when it is at a large distance from the nucleus. Ignore relativistic effects.

mass of alpha particle = 6.8 × 10⁻²⁷ kg

The nuclear radius of¹⁹⁷₇₉Au is 6.98 × 10⁻¹⁵ m.

Calculate the nuclear radius of¹⁰⁷₄₇Ag.

All nuclei have approximately the same density.

State one conclusion about the nucleons in a nucleus that can be deduced from this fact.

Two fixed charges of magnitude + Q and +3 Q repel each other with a force F. An additional charge of −2 Q is given to each charge.

What are the magnitude and the direction of the force between the charges?

Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres. The spheres are suspended by non-conducting thread.

Each sphere has a mass of 3.2 × 10⁻³ kg and a radius of 20 mm. The distance d is 40 mm.

The capacitance of a sphere of radius r is 4πε₀r.

Each sphere is charged by connecting it briefly to the positive terminal of a high-voltage supply, the other terminal of which is at 0 V. After this has been done the charge on each sphere is 52 nC.

Calculate the potential of one of the spheres.

The charged spheres in Figure 3 are at equilibrium.

Draw labelled arrows on Figure 3 to show the forces on sphere B.

Suggest a solution to one problem involved in the measurement of d in Figure 3.

Show that the magnitude of the electrostatic force on each sphere is about 4 × 10⁻³ N

A student measures the angle θ when the apparatus in Figure 3 is at equilibrium. The student records θ as 7°.

Discuss whether this measurement is consistent with the other data in this investigation.

The student says that the gravitational force between the two spheres has no significant effect on the angle at which the spheres are in equilibrium.

Deduce with a calculation whether this statement is valid.

Define the electric field strength at a point in an electric field.

Figure 2 shows a point charge of +46 C placed 120 mm from a point charge Q.

Position P is on the line joining the charges at a distance 66 mm from charge Q. The resultant electric field strength at position P is zero.

Calculate the charge Q.

Explain, without calculation, whether net work must be done in moving a proton from infinity to position P in Figure 2.

A small rubber ball coated with a conducting paint carries a positive charge. The ball is suspended in equilibrium from a vertical wall by an uncharged non-conducting thread of negligible mass. The wall is positively charged and produces a horizontal uniform electric field perpendicular to the wall along the whole of its length. Figure 3 shows that the thread makes an angle of 30° to the wall.

The thread breaks.

Explain the motion of the ball.