Magnetic Fields

Question 1

What is the magnitude of the force exerted by a magnetic field on a current-carrying wire?

What is the condition on this force?

Answer 1

F = B I l

Where:

• F = force
• B = magnetic field strength or magnetic flux density
• I = current through conductor
• l = length of conductor

Field must be perpendicular to direction of current.

Question 2

What do each of the fingers using in Fleming’s left hand rule represent?

Answer 2

Thumb: Force (or motion)

Index: External magnetic field (N to S)

Middle: current (+ to -)

Question 3

What is the definition of magnetic flux density?

Answer 3

The force on one meter of wire carrying a current of one amp at right angles to the magnetic field.

It is a vector quantity.

Question 4

What is the definition of a tesla?

Answer 4

The tesla is the unit of field strength/flux density and it is the number of flux lines per unit area:

1 tesla = 1 Wb per m² (Wb= weber = no. of flux lines)

Question 5

What is the force on a charged particle moving in an electric field?

Answer 5

F = BQv

Where:

• F = force on particle in N
• B = flux density or field strength in T
• Q = charge on the particle in C
• v = component of velocity of particle which is perpendicular to the magnetic field.

Question 6

What changes about Fleming’s left hand rule when applied to a charged particle?

Answer 6

The middle finger points in the direction that positive charge is moving i.e. if the charged particle is an electron, the middle finger would point in the opposite direction to the velocity of the particle.

Question 7

What path do charged particles trace when moving through magnetic fields?

Answer 7

As the force exerted by a magnetic field on a charged particle is always perpendicular to it’s velocity (current), the charged particle with undergo circular motion.

Question 8

What is the formula for the radius of the path of a charged particle in a magnetic field and therefore what are the effects of changing its mass, velocity charge or the field strength?

Answer 8

r = mv/BQ

• m directly proportional to r
• v directly proportional to r
• B inversely proportional to r
• Q inversely proportional to r

Question 9

Describe the structure and applications of cyclotrons.

Answer 9

• 2 hollow semicircular electrodes with a uniform magnetic field applied perpendicular to the plane of the electrodes and an alternating pd applied between the electrodes.
• Used to produce radioactive tracers or high energy beams of radiation for use in radiotherapy.

Question 10

Describe how cyclotrons work.

Answer 10

1. Charged particles are fired into one of the electrodes. The magnetic field makes them follow a semi-circular path and leave the electrode from it’s flat side.
2. The pd between the electrodes accelerates the particle across the gap until it enters the other electrode.
3. Due to the acceleration, it enters this electrode at a greater speed, the radius of its semicircular path in this electrode is greater.
4. Once it finshes completes the semi-circle, the pd direction is reversed and it is accelerated into the next electrode. This process repeats, causing the particle to spiral outwards as it speeds up before exiting the cyclotron in a straight line.

Question 11

What is magnetic flux?

Answer 11

Magnetic flux is the product of flux density (field strength) and the area in question (e.g area of a coil):

Φ = B*cosθ*A

where θ is the angle between the field and the normal to the plane of the loop/

It is measured in Wb (weber).

[The relationship between flux density and flux is analogous to that between light intensity and power.]

Question 12

What is flux linkage?

Answer 12

Flux linkage is a measure of the size of the emf induced when a coil moves relative to a magnet. As this emf is determined by the flux passing through the coil and the number of turns in the coil that cut the flux, flux linkage is given by:

linkage = B*cosθ*A*N

It is measured in Wb turns (weber-turns)

Question 13

How are flux linkage and induced voltage related?

Answer 13

The rate of change of flux linkage gives the magnitude of emf produced:

A change in flux linkage of one weber/second will induce an emf of 1 volt in a single loop of wire.

Question 14

What is Faraday’s law?

Answer 14

The induced emf is directly proportional to the rate of change of flux linkage.

Question 15

How can the magnitude of the induced emf and the flux linkage change be determined?

Answer 15

1. gradient of flux linkage (NΦ) vs t graph
2. Area under mod(emf) vs. t graph

Question 16

What is Lenz’s law?

Answer 16

The induced emf is always in such a direction as to oppose the change that caused it.

Question 17

What is the formula for induced emf?

Answer 17

ε = - N ΔΦ/Δt

Question 18

What type of current do alternators produce?

Answer 18

Alternating current: the output voltage and current change direction with every half rotation of the coil.

Question 19

What do the graphs of flux linkage and induced emf against time look like?

Answer 19

1. cos curve where coil is perpendicular to field at t=0. flux linkage = BANcos(ωt) because the angle between the normal to the coil and the field is given by θ=ωt
2. sin curve because induced emf is the negative derivative of flux linkage. ε = BAN ω sin(ωt)

Question 20

What do the oscilloscope traces of:

• ac supplies with time base on
• ac supplies with time base off
• dc supplies

look like?

Answer 20

• sin curve with max height representing maximum +ve emf
• straight vertical line as traces moves up and down between maximum =ve and -ve amplitudes
• straight horizontal line

Question 21

What are the pieces of information you can get from an oscilloscope trace?

Answer 21

• Time period, T, from horizontal distance between identical points on consecutive waves.
• Peak voltage, V_o, from maximum height above x axis
• Peak-to-peak voltage, from vertical distance between maximum +ve and -ve peaks.

Question 22

Why do we need rms voltage and how is it calculated?

Answer 22

• Ac supply w V₀ of 2V will be outputting less than 2V most of the time, so it won’t have as high a power output as a 2V dc supply. Rms voltage is used to compare ac and dc supplies.
• V_rms = V₀/sqrt(2)
• same for peak and rms current (used to calculate power output)

Question 23

What is the maximum voltage of UK mains?

Answer 23

• 230V is the V_rms value
• V₀ = sqrt(2)*V_rms = 330V

Question 24

What is the equation linking the number of turns on the coils of a transformer with the input and output voltages?

Answer 24

N_s/N_p=V_s/V_p

Question 25

How is the efficiency of a transformer calculated?

Answer 25

I_sV_s/I_pV_p

Question 26

What are the main sources of ineffciency in transformers and how are they mitigated?

Answer 26

• Eddy currents, laminating the core with layers of insulation
• Heat due to resistance in the coils, using thick, low resistance copper wire

Question 27

What are eddy currents?

Answer 27

• Looping currents within the magnetic core induced by the changing magnetic flux.
• They create a magnetic field that acts against the field that induced them, reducing the field strength. They also dissipate energy as heat.

Question 28

How do power losses arise during transmission of electrical power and how is the amount of power lost calculated?

Answer 28

Heat is dissipated in the power lines due to resistance. As P = I²R, you want to minimise current and so maximise the transmission voltage.

P = I²R, where R is given by multiplying the resistance per meter of the wire by its length.