20.1 Induced EMF

1
20.1 Induced EMF

• Induced EMF
• Faradays Law

2
Electric current gives rise to magnetic fields
B
I
Can a magnetic field give rise to a current?
The answer is yes as discovered by Michael
Faraday. This discovery lead to important
applications such a the electrical generator.
3
Michael Faraday
No current in ammeter
Battery off
4
Michael Faraday
conducting coil
ammeter
switch
Iron core
Battery
current flows
Battery switched on
5
Michael Faraday
conducting coil
ammeter
switch
Iron core
Battery
current stops
Battery on for a time
6
A changing magnetic field induces current flow
conducting coil
B
I
ammeter
switch
Iron core
Battery switches on
Battery
Current in lower coil induces a B field in the
iron
B field increases in upper coil
7
A changing magnetic field induces current flow
conducting coil
B
I
I
ammeter
switch
Iron core
Battery switches on
Battery
Current in lower coil induces a B field in the
iron
B field increases in upper coil
Changing B field induces current flow
8
A changing magnetic field induces current flow
conducting coil
B
I
I0
ammeter
switch
Iron core
Battery
After switch is on for a time B is constant B
field not changing No current flow
9
Quantitative Description
Magnetic flux FB
loop of wire with area A
units Tesla m2, weber (Wb)
10
Magnetic flux Describes the magnetic field
through an area
B field lines through a given area A Depends on
the angle area makes with the B field
When ?0, flux is maximum
When ?90o flux 0
11
Flux Description
V0
Bconstant
ammeter
I0
12
Changing magnetic flux produces an EMF (voltage
difference) that drives current
-

Vgt0
Bchanging
ammeter
I
13
Changing magnetic flux in the opposite
direction Reverses the sign of the emf.

-
Vlt0
B changing in other direction
ammeter
I
Current flows in opposite direction
14
Faradays Law
N number of turns in coil
B

-
V
ammeter
I
Minus sign refers to the direction of the emf.
This is governed by Lenzs Law. to be discussed
later.
15
magnitude of ? depends on rate of change of flux
through the loop

• To produce emf
• Change B
• Change ?, i.e rotate coil in B field

B
This can be used to generate electrical current
16
2. A circular loop with a radius of 0.20 m is
placed in a uniform magnetic field B0.85 T. The
normal to the loop makes an angle of 30o with the
direction of B. The field increases to 0.95 T
what is the change in the magnetic flux through
the loop?
Change in flux?
30o
B0.85T
B0.95T
17
4. A long straight wire carrying a current of
2.00 A is placed along the axis of a cylinder of
radius 0.50 m and length of 3.0 m. Find the total
magnetic flux through the cylinder.
B
I2.0 A
Total magnetic flux
18
8. A circular coil with a radius of 20 cm is in
a field of 0.2 T with the plane of the coil
perpendicular to the field. If the coil is pulled
out of the field in 0.30 s find the average emf
during this interval
1
N cos? A
1
pR2
B0
19
9. A 25 turn circular coil of wire has a
diameter of 1.00 m it is placed with its axis
along the direction of the earths magnetic field
of 50 x10-6 T. Then in 0.2 s it is flipped 180o.
What is the magnitude of the average emf
generated?
Change in flux?
B
??B ?B (-?B)2 ?B 2BA
?BBA
B field in
Emf?
B
-?B-BA
B field out