Gareth Jones - http://cyro.cs-territories.com /
Faraday’s law of induction
Flux, φ is represented by a m agnetic field lines and m easured in W ebers, W b.
Exam ple:Flux lines spreading
out from the end ofa bar
m agnet spread out over a
larger area.
Sm allarea, strong field
Larger area, w eaker field
M agnetic flux density, or field strength ifgiven by flux divided by area.
B=
φ
Flux, φ
A
A rea, A
Faraday’s law :Ifthe flux threading through a circuit changes then an EM F is induced. The
size ofthis EM F is proportionalto the rate ofchange offlux linkage in the circuit.
ε∝
dφ
dt
M ore turns creates
greater flux
V
V
A flux φ going through a coilofN turns generates totalflux linkage Nφ . So
ε ∝N
dφ
dt
So the flux produced can be determ ined in term s ofthe EM F produced. Lenz’s law (or
Faraday’s second law ofinduction)is w hat determ ined the direction ofthe induced EM F,
and explains how energy is conserved w hen a current is induced.
S
N
Gareth Jones - http://cyro.cs-territories.com /
The direction ofan induced EM F is alw ays such as to oppose the change offlux that
produced it. In the above circuit as the bar m agnet is m oved into the coilthe induced
current produces a north pole on the left to repelthe m agnet.
N
S
A s the m agnet the opposite happens so as to attract the m agnet (and oppose its
w ithdraw al). Therefore in Faraday’s law the constant ofproportionality is -1 to account for
Lenz’s law .
ε = −N
dφ
dt
These notes are from a lesson on 22/09/2004.