Magnetic Fields

Question 1

Define the motor effect

Answer 1

A current-carrying wired placed at a non-zero angle to the lines of force of an external magnetic field experiences a force due to the magnetic field.
The force is perpendicular to the wire and to the lines of force

Question 2

Define line of force (for a magnetic field)

Answer 2

A line of force (or magnetic field line) of a magnetic field is a line along which a free north pole would move in the field

Question 3

Describe when the force acting on a current-carrying wire in a magnetic field is:

i) greatest
ii) zero

Answer 3

i) when the wire is at right angles to the magnetic field

ii) when the wire is parallel to the magnetic field

Question 4

Define magnetic flux density and give its symbol and units

Answer 4

The magnetic flux density (B) of a magnetic field is the force per unit length per unit current on a current-carrying conductor at right angles to the magnetic field lines
F = BIL
Units: Tesla (T) - equal to 1 Nm⁻¹A⁻¹

Question 5

State the rule used to find the direction of the force in relation to the magnetic field

Answer 5

Fleming’s Left-hand Rule

• ThuMb = Motion (Force)
• First finger = Field
• SeCond finger = Current

Question 6

For a straight wire at angle θ to the magnetic field lines, give the equation for the component of the magnetic field perpendicular to the wire

Answer 6

Perpendicular component = Bsinθ
Therefore:
F = BILsinθ

Question 7

State the force experienced by a charged particle in a magnetic field moving at velocity v

Answer 7

F = Bqv

where B is the magnetic flux density and q is the charge of the particle

Question 8

State the force experienced by a stationary charged particle in a magnetic field

Answer 8

There is no magnetic force experienced by the charge if it is stationary

Question 9

What aspect of circular motion is experienced by a moving charged particle in a magnetic field?

Answer 9

The force on it is perpendicular to its velocity

Question 10

What would you use to investigate the movement of electrons in a magnetic field?

Answer 10

A Teltron Tube - an electron gun which emits electrons into a uniform magnetic field containing helium gas at low pressure which glows green when struck by an electron beam

Question 11

Relate the Kinetic energy gained by an electron by the work done on it and thus give an equation for the velocity of the electron

Answer 11

KE = Work done
½mv² = eV
mv² = 2eV
v² = 2eV / m
v = √(2eV / m)

Question 12

For an electron in a magnetic field, give the equation for the radius of an electron of charge e, in a uniform magnetic field B

Answer 12

r = mv / Be

Question 13

What path will an electron free to move in a magnetic field follow?

Answer 13

A circular path

Question 14

Relate the magnetic force experienced by a charged particle to the centripetal force of an object moving in circular moteion

Answer 14

Bqv = mv² / r
r = mv / Bq

Question 15

Give the use of a cyclotron and give a practical use

Answer 15

It accelerates charged particles

To produce high energy beams for radiation therapy

Question 16

Describe the structure of a cyclotron

Answer 16

2 hollow D-shaped electrodes (called ‘dees’) in a vacuum chamber with a uniform magnetic field applied perpendicular to the plane of the dees, and a high-frequency alternating voltage with a square waveform is applied between the dees. This creates an electric field in the space between the dees (no electric field within the dees)

Question 17

Describe how a cyclotron accelerates a charged particle

Answer 17

• Charged particles near the centre of the cyclotron are forced on a circular path by the magnetic field, causing them to emerge from the dee they were directed into.
• On emerging from the dee, the alternating voltage reverses so they are accelerated into the other dee where they are once again forced on a circular path by the magnetic field.
• The particles are accelerated by the electric field between the dees, so due to a greater velocity, their radius in the dee is larger.

Question 18

State the time period T for a charged particle to complete one full circle in a cyclotron

Answer 18

The time T for one full cycle of alternating voltage is equal to the time taken for the particle to complete 1 full circle
Hence T = 2mπ / Bq
Therefore, due to the frequency of the alternating voltage being constant,
f = 1 / T = Bq / 2πm

Question 19

Describe how a mass spectrometer works

Answer 19

Positive molecular ions are accelerated and given the same kinetic energy. Due to the difference in masses, molecular ions with greater mass have smaller velocity.
Since they are charged, they will move in a circular motion in a uniform magnetic field, so their radius can be given as:
r = mv / Bq
Therefore, molecular ions with greater mass have a greater radius in a magnetic field