General Physics II Lab
EM8 Faraday’s law of induction
General Physics II Lab
EM8 Faraday’s Law of Induction
Purpose
In this experiment, you will study Faraday’s law of induction and the mutual induction in
transformers.
Equipment and components
Science Workshop 750 interface, magnetic field sensor, voltage sensor, bar magnet, calipers,
clamp and stand, and foam (as cushion), coil of 2500 Windings, coil of 12000 Windings,
U-shaped & bar soft iron core set, oscilloscope, 100
Ω
resistor, BNC to 4mm plug cable, and
BNC to clip cable.
Background
When a bar magnet passes through a coil, the changing magnetic flux through the coil
induces an electromotive force (emf) across the coil. According to Faraday’s law of
induction, one has
d
N
dt
φ
ε
=−
,
(1)
where
is the induced electromotive force (emf),
N
is the total number of turns of the coil,
and
d
φ
/
dt
is the rate of change of the magnetic flux through the coil. The negative sign in
Eq. (1) indicates that the polarity of the induced emf is such that it tends to produce a current
that will create a magnetic flux to oppose the change of the magnetic flux through the coil
(Lenz’s law). From Eq. (1) one finds that the area under the “emf vs. time” curve represents
the total magnetic flux, because
dt
Nd
N
∫∫
.
(2)
Equation (1) can also be applied to a different situation, in which two coils are placed side by
side. In this case, a time varying current
I
(
t
) passing through the first coil (the primary coil)
can generate a time varying magnetic field
B
(
t
), which gives rise to a time varying magnetic
flux
φ
(t) =
S B
(
t
) to the secondary coil, where
S
is the cross-sectional area of the secondary
coil. As a result, an emf (or voltage) will be induced across the secondary coil. This is the
working principle of transformers. Assuming that the two coils are perfect solenoids and that
an alternating current,
I
(
t
) =
I
0
cos(
ω
t
), is used to drive the primary coil, one can readily show
that the induced emf in the secondary coil has the form
20
1
0
sin(
)
NSk nI
t
α
μωω
=
(3)
where
N
2
is the total number of turns of the secondary coil,
n
1
is the number of turns per unit
length of the primary coil,
k
is the relative permeability of the material inside the primary
coil, and
0
μ
is the permeability of free space. In Eq. (3) we introduce a correction factor
α
to
account for the decrease in the magnetic field strength from the primary coil to the secondary
coil. The magnetic field strength
10
1
B
kn
I
=
applies only to the inside of the primary coil a
the magnetic field strength in the secondary coil is assumed to be B
2
=
α
B
1
. Equation (3)
states that the induced emf varies alternatively in time and its amplitude is proportional to the
angular frequency
nd
2
f
ω
π
=
, where
f
is the frequency in units of Hz.