Electromagnetism

Question 1

State the five field line rules

Answer 1

• lines must not cross
• arrows point from north to south
• uniform field has parallel field lines
• closer lines mean stronger field
• lines start at north and end at south

Question 2

What is the right hand grip rule used for?

Answer 2

To work out the direction of the magnetic field acting on a current carrying wire

Question 3

What is Fleming’s left-hand rule used for?

Answer 3

To work out the direction of either force, current or magnetic field, when given the direction of the other two variables
Thumb = force
First finger = magnetic field
Middle finger = current

Question 4

State the equation for force on a current-carrying conductor

Answer 4

F = BIL

B stands for magnetic flux density, measured in Tesla (T)
I stands for current, measured in Amps (A)
L stands for the length of the current-carrying wire, measured in metres (m)

Question 5

What is the force on a current-carrying conductor in a magnetic field related to?

Answer 5

• the size of the current
• the magnetic field strength - or, more tenchnically the magnetic flux density
• the length of the conductor

Question 6

What is the equation for force on a current-carrying conductor when the conductor is not at right angles to the field?

Answer 6

F = BILsinθ

where θ is the angle between B and I

Question 7

Define the Tesla

Answer 7

One Tesla is the magnetic flux density required to produce a force of one Newton on a wire of length one metre carrying a current of one Amp at 90 degrees to the field

Question 8

Derive the equation for force on a single charged particle

Answer 8

Q = It or I = Q/t (1)
F = BIL (2)

Substitute (1) into (2)
F = BQL/t
F = BQ x L/t
F = BQv

Question 9

What does the BQv force do to the motion of a charged particle, and what can we infer from this?

Answer 9

The BQv force makes a charged particle move in a circle, so the force must be centripetal

Question 10

Derive an equation for the radius of a charged particle’s circular path under the action of a BQv force

Answer 10

BQv = mv²/r
BQ = mv/r
r = mv/BQ

Question 11

State four proportionalities related to the radius of a charged particle’s circular path

Answer 11

r ∝ v
r ∝ m
r ∝ 1/Q
r ∝ 1/B

Question 12

How does a velocity selector work?

Answer 12

We know that magnetic fields exert a force on moving charges. So do electric fields.
This means that placing a moving charge into a space where there is both an electric field and magnetic field will result in that charge experiencing two forces.
In a velocity selector the magnetic force on the particle acts upwards, and the electric force acts downwards, so they balance out.
The selector is long and the entrance and exit are small, so only those particles which travel through parallel to its axis make it through.

Question 13

Derive the equation for velocity of a particle in a velocity selector

Answer 13

F = QE (electric)
F = BQv (magnetic)

BQv = QE
Bv = E
v = E/B, the particles which make it through a velocity selector will have a velocity of E/B regardless of their charge

Question 14

Explain electromagnetic induction

Answer 14

A conductor is moved downwards in a magnetic field acting away from us. Since the conductor contains free electrons, moving the conductor downwards is a current upwards. We now know direction of B and I, so we can use the LHR to find the direction of the force - the electrons are forced to the left. There is an emf voltage induced across the conductor, caused by movement in the field.

Question 15

Describe and state the unit for magnetic flux density, B

Answer 15

• can be thought of as the number of lines of flux passing through an area of 1m² normal to the field
• measured in Tesla, T

Question 16

Describe and state the unit and equation for Magnetic flux, Φ

Answer 16

• can be thought of as the total amount of lines of flux in a given space
• measured in Webers, Wb
• is calculated using Φ = BA (B = Φ/A)

Question 17

Describe and state the unit for magnetic flux linkage, NΦ, BAN

Answer 17

• can be thought of as the total flux passing through a system (coil, rings)
• measured in Wb or Weber-turns

Question 18

State Faraday’s Law of electromagnetic induction

Answer 18

induced emf ∝ rate of change of flux linkage
ε ∝ ΔNΦ/Δt
usually written as
ε ∝ N x ΔΦ/Δt

Question 19

State the constant of proportionality added to Faraday’s Law, and the equation that is formed (Lenz’s Law)

Answer 19

Constant of proportionality = -1

ε = -N x ΔΦ/Δt

Question 20

State Lenz’s Law

Answer 20

Any induced emf will act in such a way that it will oppose the change in flux linkage that caused it

Question 21

Theoretically, what are the four ways in which the flux linkage could be changed?

Answer 21

Flux linkage (NΦ) = BANcosθ, therefore

• change B
• change N
• change A
• change θ

Question 22

State the equation for flux linkage, NΦ

Answer 22

NΦ = BANcosθ

Question 23

Explain how an emf is induced through the secondary coil of a transformer

Answer 23

• AC voltage across primary coil
• changing magnetic field in and around core
• change in flux linkage in secondary coil
• induced emf in secondary coil (also AC)

Question 24

State the equation relating number of turns on primary and secondary coils to voltages across them (transformer)

Answer 24

nₛ/nₚ = Vₛ/Vₚ

Question 25

If a transformer is 100% efficient what equation can we use?

Answer 25

IₛVₛ = IₚVₚ

Question 26

How could magnetism be measured?

Answer 26

• connect a search coil to an oscilloscope
• hold the search coil within a B field
• quickly withdraw the coil from the B field
  ε = -N x ΔΦ/Δt
  ε = -N x ΔBA/Δt
  ε: read off voltmeter
  N: known for that coil
  Δt: read off oscilloscope
  A: known for that coil

Question 27

State the equation for magnetic flux, Φ

Answer 27

Φ = BA