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ANSWERS
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PHYS1200
PHYSICS II
SPRING 2006
Class 7 Activity: Faraday’s Law
The relation between an induced electromotive force (emf) and a changing magnetic field is
given by Faraday’s Law. Today, you will use Faraday’s Law, a coil of wire, and a computer to
measure the strength of a magnetic field.
Let us examine Faraday’s Law to see how it can be used to measure a magnetic field. If a coil of
wire, consisting of
N
turns, experiences a changing magnetic field, the magnetic flux through it
will change. That will induce an electromotive force,
E
, as described by Faraday’s Law:
E
E
= 
= 
N
d
dt
dt
N d
B
B
Φ
Φ
,
so
If both sides of the equation on the right are integrated, the result is,
(
29
E
dt
N
d
N
t
B
B f
Bi
B i
B f
0
∫
= 
∫
= 

Φ
Φ
Φ
Φ
Φ
That is, the integral of
E
over time is equal to the change in flux through the coil times the
number of turns in the coil. Now imagine that the coil is initially in a strong magnetic field, and
ends up in a magnetic field of zero. Then the equation becomes,
(
29
i
B
i
B
t
N
N
dt
Φ
=
Φ


=
∫
0
0
E
.
However, the flux through the coil, when it is in the magnetic field, is equal to the average value
of the magnetic field in the coil,
B
av
, times the area of the coil,
A
. Since the coil is circular, this
can be written as,
2
r
B
A
B
av
av
i
B
π
=
=
Φ
.
Then the equation for the integral becomes,
2
0
r
NB
dt
av
t
=
∫
E
.
Finally, the equation can be solved for
B
av
to give,
B
dt
N
r
av
t
=
∫
E
0
2
With the help of LoggerPro,
∫
t
dt
0
E
can be measured, and
B
av
can be calculated.
1