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11.
(a) Ohm’s law combines with Faraday’s law to give
i
=
−
N
R
d
Φ
B
dt
where
R
is the resistance of the coil.
In this case,
N
= 1 (it is a single loop), and we integrate to ±nd the charge:
Z
t
0
idt
=
−
1
R
Z
t
0
d
Φ
B
dt
dt
q
(
t
)=
−
1
R
(Φ
B
(
t
)
−
Φ
B
(0))
which is equivalent to the expression shown in the problem statement. We have used little more
than the fundamental theorem of calculus; no particular assumptions have been made about how
the integrations should be performed. The result is independent of the way
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 Fall '08
 SPRUNGER
 Physics, Charge, Resistance

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