1. Magnetic fields & electromagnetic induction

2. Learning outcomes
describe magnetic fields in terms of magnetic flux & flux density
use Fleming’s left and right hand rules to describe interactions between magnetic field & current
quantitatively describe B fields around a straight current-carrying wire and a solenoid
quantitatively describe the force on a charged particle moving at right angles to a uniform B field
explain electromagnetic induction using Faraday’s & Lenz’s law
use the concept of flux linkage to explain how transformers work
describe how B fields are used in circular particle accelerators
recall the postulates and key consequences of special relativity
solve related quantitative problems

3. Teaching challenges fields are abstract
involves 3-D thinking but generally illustrated in 2-D
involves rates of change
different concepts have similar names
some physical quantities have a variety of equivalent units
students may need simple trigonometry to find the magnetic flux, or magnetic force, correctly identifying angle .

4. Permanent magnets
Magnetic field lines start and finish at poles. Physicists picture this as a ‘flow’ in magnetic circuit.
magnetic flux (phi), unit Weber
magnetic flux density B, unit Weber m-2 or Tesla
Carl Gauss & Wilhelm Weber investigated geomagnetism in 1830s, made accurate measurements of magnetic declination and inclination, built the first electromagnetic telegraph.
Magnetic flux density sometimes referred to as magnetic field strength.

5. Defining magnetic flux density
Fleming’s left-hand rule:
Force on the wire is perpendicular to both l and B.
Demo current balance: weight on one side balanced by magnetic force on other side. This is a method for measuring B.
1 Tesla = 1 N A-1m-1
Typical magnetic field strengths:
Earth’s field
bar magnet
MRI magnet B
~50 mT
0.1 T
0.2 – 3.0 T

6. Electromagnetism Electric currents have loops of B flux around them.
Current-turns produce flux.

7. Magnetic fields near currents
long straight wire
long solenoid, N turns and length l
 is the permeability of free space

8. Forces on parallel currents
parallel - attract
anti-parallel - repel

9. Forces on parallel currents
At the top wire in the diagram,
Defining the ampere (straight wires of infinite length)
If the current in each wire is exactly 1 A,
and the distance between the wires is 1 m,
then the force on each metre length of the wires will be 2 x 10-7 N.
Practice questions: TAP Forces on currents
Demo forces on parallel and anti-parallel currents.

10. Force on a moving charge
Demonstration: fine beam tube
uniform B-field at right angles to an electron beam with v
F is perpendicular to v, so the beam travels in a circular path.
Cyclotron invented by E Lawrence, Now replaced by synchrotron, in which B-field magnetic field E-field are both carefully synchronized with the travelling particle beam.

11. Fluxes and forces
Michael Faraday (experimenting in 1830s at the Royal Institution) pictured magnetic field lines as flexible and elastic
magnetic attraction: field lines try to get shorter & straighter
magnetic repulsion: field lines cannot cross

12. Faraday’s law of induction
Induced emf is proportional to rate of ‘cutting’ field lines.
N is number of turns on the secondary coil. N is its flux linkage.
Induced emf is proportional to rate of change in coil’s flux linkage.
NOTE: Eddy currents are induced in iron core linking primary and secondary coils. These can be reduced by laminations in core.

13. No relative motion means no induced emf.
can be:
1 the flux cut by a moving wire
2 the change in flux due to a magnet moving
3 the change in flux due to a stationary electromagnet which is changing in strength
No relative motion means no induced emf.
Under what conditions is there an induced current?

14. Experiments Force on a current-carrying wire Current balance
Investigating fields near currents (using a Hall probe)
Investigating electromagnetic induction
Faraday’s law
Jumping ring

15. Practice questions (Adv Physics) Changes in flux linkage
(Adv Physics) Flux or flux linkage?
TAP Rates of change
(Adv Physics) Graphs of changing flux and emf

16. Endpoints
rotating coil (AC) generator:
motors produce a ‘back emf’