Download Chapter 31

Chapter 31
Faraday’s Law
Dr. Jie Zou
PHY 1361
1
Outline

Faraday’s law of induction




Some observations and Faraday’s
experiment
Faraday’s law of induction
Some applications of Faraday’s law of
induction: An electric guitar
Motional emf
Dr. Jie Zou
PHY 1361
2
Some observations

Observations:




Dr. Jie Zou
(a) When a magnet is moved toward a
loop of wire connected to a galvanometer,
the galvanometer deflects, indicating an
induced current in the loop.
(b) When the magnet is held stationary,
there is no induced current in the loop,
even when the magnet is inside the loop.
(c) When the magnet is moved away from
the loop, the galvanometer deflects in the
opposite direction, indicating an induced
current opposite that in part (a).
A current is set up even though no
batteries are present in the circuit! Such a
current is called an induced current and
it is produced by an induced emf.
PHY 1361
3
Faraday’s experiment

Observations:




Faraday’s conclusion:


Dr. Jie Zou
(1) At the instant the switch is closed,
the galvanometer needle deflects in
one direction and then returns to zero.
(2) At the instant the switch is opened,
the needle deflects in the opposite
direction and again returns to zero.
(3) The galvanometer reads zero when
there is either a steady current or no
current in the primary circuit.
An electric current can be induced in a
circuit by a changing magnetic field.
An induced emf is produced in the
secondary circuit by the changing
magnetic field.
PHY 1361
4
Faraday’s law of induction

Faraday’s law of induction: The emf
induced in a circuit is directly proportional to
the time rate of change of the magnetic flux
through the circuit.
d B
 
dt



Dr. Jie Zou
Here,  B   B  dA is the magnetic flux through
the circuit.
(1) For a planar loop in a uniform magnetic field:
d
   BA cos  
dt
(2) For a coil consisting of N loops:
d B
  N
dt
PHY 1361
5
Applications of Faraday’s law
An electric guitar
Dr. Jie Zou
PHY 1361
6
Examples


Dr. Jie Zou
Example 31.1: A coil consists of 200 turns of
wire. Each turn is a square of side 18 cm, and a
uniform magnetic field directed perpendicular to
the plane of the coil is turned on. If the field
changes linearly from 0 to 0.50 T in 0.80 s, (a)
what is the magnitude of the induced emf in the
coil while the field is changing? (b) If the ends of
the coil are connected to a circuit and the total
resistance is 2.0 , what is the current in the
coil?
Example 31.2: A loop of wire enclosing an area A
is placed in a region where the magnetic field is
perpendicular to the plane of the loop. The
magnitude of B varies in time according to B =
Bmaxe-at, where a is some constant. Find the
induced emf in the loop as a function of time.
PHY 1361
7
Motional emf


Motional emf: The emf
induced in a conductor moving
through a constant magnetic
field.
Consider a straight conductor of
length l moving with a velocity v
through a uniform magnetic field
B directed perpendicular to v:



Dr. Jie Zou
|| = Blv
I = Blv/R
If v is constant, power delivered by
the applied force = power delivered
to the resistor=2/R=B2l2v2/R.
PHY 1361
8
Examples


Dr. Jie Zou
Example 31.4: A conducting bar of length l
rotates with a constant angular speed  about a
pivot at one end. A uniform magnetic field B is
directed perpendicular to the plane of rotation.
Find the motional emf induced between the ends
of the bar.
Example 31.5: The conducting bar moves on two
frictionless parallel rails in the presence of a
uniform magnetic field directed into the page.
The bar has mass m and its length is l. The bar
is given an initial velocity vi to the right and is
released at t = 0. Using Newton’s laws, find the
velocity of the bar as a function of time.
PHY 1361
9