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.

cos
BA
A
B 

 

5. Defining magnetic flux density
B =
F
Il
Typical magnetic field strengths:
Earth’s field bar magnet MRI magnet
B ~50 mT 0.1 T 0.2 – 3.0 T
Fleming’s left-hand rule:
Force on the wire is perpendicular to both l and B.

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
r
I
B


2
0

I
l
N
B 0


-2
7
NA
10
4 

 

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

9. Forces on parallel currents
r
I
I
BI
l
F
r
I
B




2
2
2
1
0
1
2
0



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

10. 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.
Force on a moving charge

sin
qvB
F
qvB
lB
t
q
IlB
F



 


r
mv
qvB
2


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.
emf E = -N dF
dt

13. 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?
dF
dt can be:

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’
t
BAN 
cos
emf 
