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PHYS809 Class 28 Notes
Time varying fields and Maxwell’s equations
Faraday experimentally determined that a transient current is induced in a circuit if (a) a steady current
in a nearby circuit is switched on or off, (b) a nearby circuit with a steady current is moved relative to the
first circuit, or (c) a permanent magnet is moved in or out of the circuit. These experiments showed that
changes in magnetic field can cause current flow. Faraday’s result can be summarized as a relation
between the magnetic flux threading the circuit
,
S
F
dS
=
⋅
∫
B n
(28.1)
and a quantity called the
electromotive force
around the circuit
.
C
d
=
⋅
∫
E l
E
(28.2)
Note that for an electrostatic situation,
0
∇×
=
E
implies that the electromotive force (emf) is always
zero.
In SI units, Faraday’s law is
.
dF
dt
= 
E
(28.3)
The physical significance of the minus sign is that the current (if any) that results from the induced emf is
the direction that opposes the change in the magnetic flux.
Faraday’s law in the form of equation (28.3) is quite general and includes the case in which the circuit
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 Fall '11
 MacDonald
 Current

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