[Maximum number: 1]

An electron moves with uniform circular motion in a region of magnetic field. Which diagram shows the acceleration a and velocity v of the electron at point P ?

A

B

C

D

[Maximum number: 6]

There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is connected by an electronically-conducting cable to another smaller satellite Y .

not to scale

(a)

The cable between the satellites cuts the magnetic field lines of the Earth at right angles.

Explain why satellite X becomes positively charged.

[ 3 ]

(b)

Satellite X must release ions into the space between the satellites. Explain why the current in the cable will become zero unless there is a method for transferring charge from X to Y .

[ 3 ]

(a)

The long straight conductor is formed into a coil consisting of two separate turns, X and Y . The coil hangs with its axis vertical.

Assume that the turns of the coil each behave as a long straight conductor.

[ 3 ]

(i)

The current in the coil is 15 A and the circumference of one turn is 0.48 m . In order to restore X and Y to their original separation, a mass of $2.8 \times 10^{-4} \mathrm{~kg}$ is suspended from turn Y . Estimate the magnetic field strength at X due to Y .

A3. This question is about radioactivity.

Caesium-137 ( ${ }_{55}^{137} \mathrm{Cs}$ ) is a radioactive waste product with a half-life of 30 years that is formed during the fission of uranium. Caesium-137 decays by the emission of a beta-minus $\left(\beta^{-}\right)$ particle to form a nuclide of barium (Ba).

[ 3 ]

(a)

A particle of mass m and positive charge q moves on a circular path with speed v in a vacuum. A uniform magnetic field B is directed into the plane of the page.

[ 2 ]

(i)

Show that the radius R of the circular path is given by $R=\frac{m v}{q B}$ .

[ 1 ]

(ii)

Suggest why the speed of the particle stays constant, even though a force acts on the particle.

[ 1 ]

(b)

The particle in (b), now moving in a region of magnetic field in air, follows the path shown.

Explain the shape of this path.

[ 2 ]

(a)

A particle of mass m and positive charge q moves on a circular path with speed v in a vacuum. A uniform magnetic field B is directed into the plane of the page.

[ 2 ]

(i)

Show that the radius R of the circular path is given by $R=\frac{m v}{q B}$ .

[ 1 ]

(ii)

Suggest why the speed of the particle stays constant, even though a force acts on the particle.

[ 1 ]

(b)

The particle in (b), now moving in a region of magnetic field in air, follows the path shown.

Explain the shape of this path.

[ 2 ]

[Maximum number: 4]

Two oppositely charged parallel plates are a distance 8.0 cm apart. The potential difference between the plates is 120 V . An alpha particle is placed on the positively charged plate and released from rest. Gravity is ignored.

(a)

(i)

Show that the acceleration of the alpha particle is about $7 \times 10^{10} \mathrm{~ms}^{-2}$ .

[ 2 ]

(b)

A magnetic field directed into the plane of the page is now established between the plates. An alpha particle enters the region between the plates with a horizontal speed of $5.0 \times 10^{5} \mathrm{~m} \mathrm{~s}^{-1}$ . The particle is not deflected.

Calculate the magnitude of the magnetic field.

[ 2 ]

[Maximum number: 5]

Two oppositely charged parallel plates are a distance 8.0 cm apart. The potential difference between the plates is 120 V . An alpha particle is placed on the positively charged plate and released from rest. Gravity is ignored.

(a)

(i)

Show that the acceleration of the alpha particle is about $7 \times 10^{10} \mathrm{~ms}^{-2}$ .

[ 2 ]

(b)

A magnetic field directed into the plane of the page is now established between the plates. An alpha particle enters the region between the plates with a horizontal speed of $5.0 \times 10^{5} \mathrm{~m} \mathrm{~s}^{-1}$ . The particle is not deflected.

Calculate the magnitude of the magnetic field.

[ 2 ]

(c)

The alpha particle in (c) is replaced by an electron. The electron enters the region between the plates with the same velocity as the alpha particle.

Draw, on the diagram, the path of the electron.

[ 1 ]

(a)

Two parallel current-carrying wires have equal currents in the same direction. There is an attractive force between the wires.

[ 1 ]

(i)

Identify the nature of the attractive force recorded by an observer stationary with respect to the wires.

[ 1 ]

[Maximum number: 2]

A wire carries an electric current. An external electron e moves with the drift velocity v of the electrons in the wire. Observer O is at rest relative to the wire.

(a)

State and explain the nature of the electromagnetic force acting on electron e in the frame of reference of

[ 2 ]

(i)

observer O .

[ 2 ]

[Maximum number: 1]

The ampere is defined in terms of

A

power dissipated in a wire of known length, cross-sectional area and resistivity.

B

potential difference across a resistance of known value.

C

number of electrons flowing past a point in a circuit in a given time.

D

force per unit length between parallel current-carrying conductors.