Electric potential

A particle has mass m and charge q.

The particle is moved a distance d through a potential difference V.

What is the change in electric potential energy?

The diagram shows an electron in an electric field represented by equipotentials.

Which arrow shows the direction of the electric force on the electron?

The electric potential at a point in an electric field is −4.0 V.

Explain what is meant by this statement.

Figure 9 shows an arrangement for confining groups of electrons to small regions inside a block of gallium arsenide.

Electrons can only move along the line PQ in the block.

When a suitable electric potential is applied to the electrodes, the electrons are confined to the regions shown in Figure 9.

The graph in Figure 9 shows how the electric potential V varies with

Determine, using the graph in Figure 9, the maximum magnitude of the electric field. State an appropriate unit for your answer.

An electron at rest at x = 300 nm gains kinetic energy and moves to x = 800 nm.

Determine the minimum kinetic energy required by the electron.

One of the confined electrons is at x = 350 nm.

Discuss the subsequent motion of this electron due to the variation in electric potential shown in Figure 9. Assume that the electron starts from rest.

Which diagram shows a distribution of charge where the electric potential at P and the electric field at P are both zero?

Figure 4 shows a spark detector used to detect alpha particles.

The detector consists of a metal mesh placed 5.0 mm above a wire. A potential difference of 4000 V is applied between the mesh and the wire.

Molecules in the air between the mesh and the wire are ionised by an alpha particle and a spark is produced.

Figure 5 shows equipotentials between the mesh and the wire.

Figure 5 shows a dashed line between the mesh and the wire.

Sketch on Figure 6 a graph to show how the magnitude E of the electric field strength varies with the distance d from the mesh along this dashed line. No values are required on the E axis.

An alpha particle passes through the mesh. The alpha particle ionises an argon atom at P on Figure 5, releasing one electron. The electron and the argon ion have no kinetic energy at P. The electron then travels to the wire and the argon ion travels to the mesh.

Assume that the air has no effect on the motion of the electron or on the motion of the argon ion.

mass of argon ion = 6.64 × 10⁻²⁶ kg

In practice, the air does affect the motion of the electron and the motion of the argon ion.

Suggest how the presence of air between the mesh and the wire changes the ratio in Question 04.2. No numerical detail is required.

The alpha source in Figure 4 is moved to different heights h above the mesh.

Figure 7 shows how the number of sparks N produced in 10 minutes varies with h. No sparks are produced when the source is not present.

Student A suggests that the spark rate obeys an inverse-square law. Student B suggests that the spark rate decreases exponentially with h.

Determine whether either student is correct.

The graph shows the variation of electric field strength E surrounding a charged sphere of radius R. The distance from the centre of the sphere is r.

The total area under the curve from R to infinity is

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.

A particle of mass m and charge Q is accelerated from rest through a potential difference V. The final velocity of the particle is u. A second particle of mass and charge 2Q is accelerated from rest through a potential difference 2 V.

What is the final velocity of the second particle?

The diagram shows a uniform electric field of strength 15 V m. The length RS is perpendicular to the field and the line ST is parallel to the field.

What is the total change in electrical potential energy for a charge of 3.0 μC moving from R to T ?

Figure 9 shows a cyclotron. A proton is released from rest and is accelerated each time it reaches the gap between two horizontal ‘dees’ D₁ and D₂. Between these accelerations the proton moves at constant speed. A vertical magnetic field of flux density B acts over the dees so that the proton follows a semicircular path in each dee.

The dees are connected to an alternating potential difference (pd). This pd is adjusted so that the proton is always accelerated by the peak electric field as it crosses the gap between the dees.

Explain why the proton travels in a semicircular path in a dee.

The peak pd of the alternating supply is 10.0 kV. The proton leaves the cyclotron with kinetic energy of 14 MeV.

Determine the number of times the proton moves across the gap before it leaves the cyclotron.

The radius of the outermost semicircular path of the proton is R and the proton leaves with a maximum kinetic energy E_k.

Show that E_k is given by

A hospital decides to purchase a cyclotron in order to manufacture its own radioactive isotopes using high-speed protons. The required minimum kinetic energy of the emerging protons is 11 MeV. The cost of a cyclotron is approximately proportional to E_k^1.5. The cost of a 10 MeV cyclotron is about £2.3 million. Table 1 gives information for three cyclotrons X, Y and Z.

Deduce which cyclotron X, Y or Z will satisfy the energy requirement for the lowest cost. Go on to determine the approximate cost of this cyclotron.

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.

Two charged particles P and Q are separated by a distance of 120 mm. X is a point on the line between P and Q where the electric potential is zero.

What is the distance from P to X ?

An isolated spherical conductor is charged. The conductor has a radius R and an electric potential V. The electric field strength at its surface is E.

Point T is a distance 2 R from the surface.

What are the electric field strength and electric potential at T ?

O is the centre of a negatively charged sphere.

K and L are two points at a distance r₁ from O. M and N are two points at a distance r₂ from O.

Which statement is true?

The diagram shows the path of a proton being deflected by the nucleus of an atom. Point P is the position of the proton when it is closest to the nucleus.

What is not true about the proton along its path at P ?

At a distance L from a fixed point charge, the electric field strength is E and the electric potential is V.

What are the electric field strength and the electric potential at a distance 3 L from the

Which diagram shows lines of equipotential in steps of equal potential difference near an isolated point charge?

A positive charge of 2.0 × 10⁻⁴ C is placed in an electric field at a point where the potential is +500 V.

What is the potential energy of the system?

Two charges P and Q are 100 mm apart. X is a point on the line between P and Q where the electric potential is 0 V.

What is the distance from P to X ?

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.

1.5 mJ of work is done when a charge of 30 µC is moved between two points, M and N, in an electric field.

What is the potential difference between M and N ?

The ionisation potential for the atoms of a gas is V. Electrons of mass m and charge e travelling at a speed v can just cause ionisation of atoms in the gas.

What is v ?

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.

A charged spherical conductor has a radius r. An electric field of strength E exists at the surface due to the charge.

What is the potential of the spherical conductor?

Four positive charges are fixed at the corners of a square as shown.

The total potential at the centre of the square, a distance d from each charge, is .

What is the magnitude of the fourth charge?

State what is represented by gravitational field lines.

Figure 6 shows the gravitational field above a small horizontal region on the surface of the Earth.

Suggest why the field lines converge over a small area at K.

A ball travelling at constant speed passes position J moving towards position K in Figure 6.

Assume friction is negligible.

Explain any change in the speed of the ball as it approaches K.

Figure 7 shows lines of force for the electric field surrounding two charged objects L and M.

Explain why the lines of force shown in Figure 7 cannot represent a gravitational field.

State which object L or M has a charge with the greater magnitude.

State which object L or M has a positive charge.

Draw, on Figure 7, an equipotential line that passes through point N. Do not extend your line beyond the given field lines.