Download Flux or flux linkage? - Institute of Physics

Magnetic fields &
electromagnetic induction
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
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 .
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
  B A  BAcos

Carl Gauss & Wilhelm Weber investigated geomagnetism in 1830s,
made accurate measurements of magnetic declination and
inclination, built the first electromagnetic telegraph.
Defining magnetic flux density
Fleming’s left-hand rule:
Force on the wire is perpendicular to both l and B.
F
B=
Il
Typical magnetic field strengths:
Earth’s field bar magnet
B
~50 mT
0.1 T
MRI magnet
0.2 – 3.0 T
Electromagnetism
Electric currents have loops of B flux around them.
Current-turns produce flux.
Magnetic fields near currents

I
• long straight wire B 
2r
0
• long solenoid, N turns and length l
N
B I
l
0

 4 10 NA is the permeability of free space
7
-2
Forces on parallel currents
parallel - attract
anti-parallel - repel
Forces on parallel currents
At the top wire in the diagram,
I
B
2r
F
II
 BI 
l
2r
0
2
0
1
2
1
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
Force on a moving charge
q
F  IlB  lB  qvB
t
F  qvB sin 



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.
mv
qvB 
r
2
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
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.
emf E = -N dF
dt
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.
dF
dt
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?
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
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
Endpoints
• rotating coil (AC) generator: emf
• motors produce a ‘back emf’
  BANcost