Section 7.5: Magnetic Fields

Question 1

Define magnetic flux density

Answer 1

It is a measure of the strength of a magnetic field, symbol B and unit Tesla (T).

Question 2

Define one Tesla

Answer 2

A force of 1 Newton on 1 metre of wire carrying 1 ampere of current perpendicular to a magnetic field.

Question 3

What happens when current flows through a wire in terms of fields?

Answer 3

A magnetic field is induced, where the field lines form concentric circles around the wire.

Question 4

What happens when a current-carrying wire is placed in a magnetic field?

Answer 4

If the field is perpendicular to the current, a force will be exerted on the wire. If the field is parallel to the current, nothing will happen since no component of the field is perpendicular to the current.

Question 5

In what direction do magnetic field lines go?

Answer 5

From north to south.

Question 6

Why does a force act on a current-carrying wire in a magnetic field?

Answer 6

Because a force acts on charged particles moving in a magnetic field, in this case the electrons of the current flowing through the wire.

Question 7

How do charged particles move in a magnetic field and why?

Answer 7

They will move in a circular path since the force they experience is always perpendicular to their motion, which is the condition for circular motion.

Question 8

How do you find the radius of a charged particle’s motion in a magnetic field?

Answer 8

Set the magnetic force equal to centripetal force, then rearrange to get r as the subject.

Question 9

Explain how a cyclotron works

Answer 9

It is formed of two semi-circular electrodes called ‘dees’ with a uniform magnetic field acting perpendicular to the plane of the dees, a small gap between the electrodes, and a high frequency alternating voltage applied between the electrodes.

A particle begins at the centre and moves in a circular path through one of the dees. Once it reaches the edge of the dee again, it will be accelerated across the gap by the electric field, increasing the radius of the particle’s path in the other dee. Then when it reaches the gap again, the electric field changes direction to accelerate the particle in the opposite direction.

This is repeated until the particle reaches the desired speed, at which point it leaves the cyclotron.

Question 10

What are some uses of cyclotrons?

Answer 10

Producing ion beams for radiotherapy, and radioactive tracers.

Question 11

Define magnetic flux

Answer 11

A value which describes the magnetic field or magnetic field lines passing through a given area when the area and field lines are perpendicular, calculated by finding the product of the magnetic flux density and the given area, symbol φ​.

Question 12

Define magnetic flux linkage

Answer 12

The magnetic flux multiplied by the number of turns of the coil, symbol NΦ.

Question 13

What is electromagnetic induction?

Answer 13

When a conducting rod moves relative to a magnetic field, the electrons in the rod will experience a force due to being charged particles, and build up on one side of the rod, causing an emf to be induced in the rod.

This also occurs with a bar magnet moving relative to a coil of wire - if the coil forms a circuit an emf is induced.

Question 14

What is Faraday’s law?

Answer 14

The magnitude of induced emf is equal to the rate of change of flux linkage.

Question 15

What is Lenz’s law?

Answer 15

The direction of induced current is such as to oppose the motion causing it.

Question 16

How can you demonstrate Lenz’s law?

Answer 16

Compare the speed of a magnet falling through a coil of wire and a magnet falling the same height but not through a coil of wire.

1. As the magnet approaches the coil of wire, there is a change of flux through the coil and so an emf and current is induced.
2. Due to Lenz’s law, the direction of induced current is such as to oppose the motion causing it, so the pole at the top of the coil will be the same as the pole of the magnet approaching the coil, which will cause the magnet to slow down due to the electrostatic force of repulsion.
3. As the magnet passes through the middle of the coil there is no change in flux through the coil and so no emf or current is induced.
4. As the magnet starts to leave the coil, there is a change of flux and so a current is induced that opposes the motion of the magnet, so an opposite pole is induced at that end of the coil, which slows down the magnet due to the electrostatic force of attraction.

Question 17

Derive the general formula for the magnitude of emf induced by a straight conductor, length L, moving through a magnetic field of flux density B.

Answer 17

The equation for the distance travelled by the conductor will be:

s = vΔt

If we consider the distance travelled to be the width, we can find the area:

A = LvΔt

Since ΔΦ = BA, that means:

ΔΦ = BLvΔt

Substituting it into the equation for Faraday’s law, we get:

ε = BLv

Question 18

How do you get from peak-to-peak voltage to root mean squared voltage?

Answer 18

Divide the peak-to-peak voltage by √2

Question 19

Describe a transformer

Answer 19

Transformers are used with alternating currents to change the size of their voltage. The consist of an iron core and two coils of wire: the primary coil, connected to the input voltage, and the secondary coil, connected to the output voltage. The primary coil provides a changing magnetic field, which passes through the iron core and interacts with the secondary coil, inducing a voltage in the secondary coil.

Question 20

Describe a step-up transformer

Answer 20

A transformer that increases the input voltage by having more turns on the secondary coil than the primary coil.

Question 21

Describe a step-down transformer

Answer 21

A transformer that decreases the input voltage by having fewer turns on the secondary coil than the primary coil.

Question 22

State the ways in which the efficiency of a transformer can be increased

Answer 22

• Use a laminated iron core to minimise the effect of eddy currents
• Make the core out of a high resistivity metal to minimise the effect of eddy currents
• Use a soft iron core to allow easy magnetisation and demagnetisation, minimising energy loss
• Use thick wires with a low resistance to minimise energy loss through heating

Question 23

Explain eddy currents and how they can be reduced

Answer 23

Eddy currents form in the core of a transformer, and are induced by the changing magnetic field in the primary coil. Due to Lenz’s law, they oppose the change which caused them, meaning they reduce the field’s flux density and generate heat, leading to energy loss. Laminating the core, meaning using layers of iron between layers of an insulator, reduces the amplitude of eddy currents as they cannot pass through the insulator.

Question 24

How is power lost in transmitting electricity over long distances, and how can this be minimised?

Answer 24

When transferring electrical power, the power lost due to resistance is I^2 x R. So to minimise the power lost, current must be minimised. Since P = I x V, a higher voltage equals a lower current, so the voltage is stepped up for long distance transmission.

Question 25

What is the rms voltage of the electricity supplied to UK homes?

Answer 25

230V