Consider a conductor moving in a
magnetic field….
Induction
The conductor is filled with mobile
charges (by definition).
Each charge is a moving charge in a
X
Xfield, and
X will therefore
X
X have
magnetic
a force exerted on it.
X
X
X
X
X
X
+X
+
X
+
X
+
X
This causes,
(induces)
aX
current Xto
X
X
X
flow.
This was quite possibly the
most important single event
of the 19th century.
Henry
Faraday
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
The conductor is filled with mobile
charges (by definition).
We call this
X
X
phenomena
Electromagnetic
Induction
X
X
X
X
X
+X
X
X
+
X
X
+
X
X
X
X
X
X
+
X
X
Who was the guy who did it the other way
around? Discovered magnetism from
electricity?
In 1831 Michael Faraday in England,
and Joseph Henry in the United States
independently discovered electromagnetic
induction…the production of electricity
from magnetism.
1
Lentz’s Law:
The direction of an induced current
is always such that its own magnetic
field opposes the magnetic field
responsible for producing it.
An electromotive force
(emf) is produced in a
conductor whenever it cuts
across magnetic field lines.
No emf arises from motion
parallel to a magnetic field.
Lentz’s law is a statement of the
Law of Conservation of Energy
Drop a magnetic through a conducting
ring.
S
A current will be
induced in the ring.
N
Consider a
charge Q in
the ring
As the loop is pulled out of
the field, a current will be
induced in the loop.
Drop a magnetic through a conducting
ring.
The
secondary
magnetic
lines of force
always
oppose the
creating lines
of force.
N
Consider the force on
this leg of the loop
N
pull
S
Induced force
opposes original
force
N
pull
S
S
2
Induced emf and Magnetic
Flux
• Electric current produces magnetic
fields.
• An electric current can be produced by
a changing magnetic field (a current
cannot be produced by a steady
magnetic field).
Faraday’s Law of Induction
emf = −NA
Where
ΔB sin θ
Δt
Emf = in Volts
N = # of turns
ΔB = change in magnetic field (Tesla)
A = area of loop or wire (m2)
θ = angle between B and the direction
perpendicular to the plane of the loop.
Note: The minus sign is included only to indicate the
polarity (direction) of the induced emf (Lenz’s Law)
Induced emf and Magnetic
Flux
• The induced emf is produced by a change in
the MAGNETIC FLUX.
• A current is set up in a wire or circuit as long
as there is relative motion between the
magnet and the loop.
• The induced emf (volts) in a circuit is
proportional to the # of loops in the circuit,
and the rate of change of the magnetic flux.
Example: A coil is wrapped with two-hundred turns of wire an a square
frame with 18 cm sides. Each turn has the same area, equal to that of the
frame, and the total resistance of the coil is 2.0 Ω. A uniformly magnetic
field is applied perpendicular to the plane of the coil. If the field changes
uniformly from 0.50 to 0.00 T in 0.80 sec,
(a) Find the magnitude of the emf in the induced coil while the field is
changed.
N = 200 turns
A = (0.18m)2 = 0.0324 m2
At t=0, B=0.50T
At t = 0.80s, B = 0.00 T
emf = -(200)(0.0324 m2)(-0.5T)/0.80s
emf = 4.1 V
Example: A coil is wrapped with two-hundred turns of wire an a square
frame with 18 cm sides. Each turn has the same area, equal to that of the
frame, and the total resistance of the coil is 2.0 Ω. A uniformly magnetic
field is applied perpendicular to the plane of the coil. If the field changes
uniformly from 0.50 to 0.00 T in 0.80 sec,
(b) Find the magnitude of the induced current in the coil while the field is
changing..
V = IR
I = V/R
I = 4.05 V / 2.0 Ω
I = 2.025 A ~ 2.0A
3