ELECTROMAGNETISM

Question 1

Magnetic flux density/ field strength

Answer 1

The density of the field lines aka the ‘strength’ of the field in a given area. Units: Tesla (T) 1T = 1NA^-1 m^-1.

Question 2

Magnetic flux

Answer 2

The magnetic flux density passing through an area that is perpendicular to the magnetic field ϕ = BAcosθ where θ is the angle between the magnetic field and the perpendicular to the area.

Question 3

Magnetic flux linkage Nϕ

Answer 3

The magnetic flux multiplied by the number of turns in the coil Units: Weber (Wb) 1Wb =1Tm^2 = 1NA-1 m^2.

Question 4

Faraday’s law

Answer 4

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

Question 5

Lenz’s law

Answer 5

The direction of the emf induced will oppose the change that created it (this is due to conservation of energy)

Question 6

How does a Cyclotron work?

Answer 6

1. Charged particles/ions released in centre.
2. Ions are accelerated towards dee due to the electric field across the dees causing a potential difference between them and a resultant force in the same direction as velocity.
3. Under influence of magnetic field when inside the dees, it moves in a circular motion as the resultant force is perpendicular to the velocity.
4. When the ions reach the gap again, the alternating potential difference reverses and this accelerates the ion source back towards the first dee.
5. It enters dee 2 with a higher speed and has an increased radius as 𝑟=𝑚𝑣𝐵𝑞
6. The ion source moves back towards the gap and process is repeated until it exits from the cyclotron.
7. The time spent in each dee is the same and so the frequency of the alternating voltage remains constant. It should be switched every half-circle.

Question 7

Key features of a cyclotron:

Answer 7

1. Set up in vacuum to minimise energy loss in collisions with air particles.
2. Ion source to be accelerated.
3. Alternating potential difference to accelerate ion source.
4. Uniform magnetic field to accelerate ions in a circular path.

Question 8

Limitations of a cyclotron:

Answer 8

1. When particles move near speed of light, mass increases.
2. Thus particles will spend longer in each dee.
3. The AC voltage will reverse too early and synchronisation will be lost.
4. Occurs at energies of roughly 20MeV.

Question 9

Explain how a linac accelerates charged particles

Answer 9

1. Charged particle is accelerated by an electric field.
2. The alternating potential difference means that as the charged particle emerges from one tube the next has the opposite potential and hence applies a resultant force in the direction of motion and accelerates it.
3. The potential difference switches at a constant frequency so the time in each drift tube is fixed.
4. The length of the drift tube increases as the speed is greater so the distance the charge travels in a fixed time increases.