- Faraday's experiment demonstrated that a changing magnetic field can induce an electric current in a nearby conductor. He showed this by inducing currents in a secondary coil wrapped around a ring using the changing magnetic field from a primary coil with a switch-controlled current. - Faraday's law of induction states that the induced emf in a circuit is directly proportional to the rate of change of the magnetic flux through the circuit. A changing magnetic field induces currents that oppose the change according to Lenz's law. - Examples are given demonstrating how Lenz's law predicts the direction of induced currents based on producing a magnetic field that opposes the change causing it.

1. Prepared by
Md. Amirul Islam
Lecturer
Department of Applied Physics & Electronics
Bangabandhu Sheikh Mujibur Rahman Science &
Technology University, Gopalganj – 8100

3. An electric current can be induced in a circuit by a changing
magnetic field.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 980
(a) When a magnet is moved
toward a loop of wire connected
to a galvanometer, the
galvanometer deflects as shown,
indicating that a current is
induced 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.
Law

4. Faraday’s Experiment:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 980
A primary coil is connected to a switch and a battery. The coil is
wrapped around a ring, and a current in the coil produces a
magnetic field when the switch is closed. A secondary coil also is
wrapped around the ring and is connected to a galvanometer.

5. Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 980
No battery is present in the secondary circuit, and the
secondary coil is not connected to the primary coil. Any current
detected in the secondary circuit must be induced by some
external agent.
At the instant the switch is closed, the galvanometer needle
deflects in one direction and then returns to zero. At the instant
the switch is opened, the needle deflects in the opposite direction

6. Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 980
and again returns to zero. Finally, the galvanometer reads zero
when there is either a steady current or no current in the
primary circuit.
when the switch is closed, the current in the primary circuit
produces a magnetic field in the region of the circuit, and it is
this magnetic field that penetrates the secondary circuit.

7. Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 980
Furthermore, when the switch is closed, the magnetic field
produced by the current in the primary circuit changes from
zero to some value over some finite time, and it is this changing
field that induces a current in the secondary circuit.
This experiment conducted by Michael Faraday proves that a
changing electric field can induce electric current.

8. Mathematical Expression of Faraday’s Law:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 982
The emf induced in a circuit is
directly proportional to the time
rate of change of the magnetic flux
through the circuit.
Here, ФB = B.dA is the magnetic
flux through the circuit.
Fig: Conducting loop that encloses an
area A in the presence of a uniform
magnetic field B. The angle between
B and the normal to the loop is θ.
** We will get the explanation of the
negative sign in the equation, in
Lenz’s Law.

9. Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.1, Page – 982
If the circuit is a coil consisting of N
loops all of the same area and if ФB is
the flux through one loop, an emf is
induced in every loop; thus, the total
induced emf in the coil is given by the
expression,
According to the figure, ФB = BAcosθ
then the equation can be expressed as,

11. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.6, Page – 943
Right hand rule:
Put your four fingers on the
direction of loop current I. The
direction of thumb will indicate
to the magnetic field B.
Screw rule:
Put a screw on the center of the
loop. Move the screw on the
direction of current. The motion
of the screw will indicate the
direction of magnetic field.

13. The polarity of the induced emf is such that it tends to produce
a current that creates a magnetic flux to oppose the change in
magnetic flux through the area enclosed by the current loop.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.3, Page – 988
Law
Example I:
(a) When the bar moves to the right, by Lenz’s law, the induced current must be
counterclockwise so as to produce a counteracting magnetic flux directed out of the page.
(b) When the bar moves to the left, the induced current must be clockwise.

14. Explanation:
Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.3, Page – 988
As the bar moves to the
right, the magnetic flux
through the area enclosed
by the circuit increases
with time because the
area increases. According
to Lenz’s law the induced
current must be directed so
that the magnetic flux it produces opposes the change in the external
magnetic flux. As the external magnetic field is inward to the board, the
magnetic field produced by the induced current will be outward direction.
According to the right hand rule (or screw rule), the direction of the
induced current will be counterclockwise direction for a outward magnetic
field.
In second case, the current direction will be clockwise because in this case
the magnetic field due to current I should be inward direction to minimize
the decreasing magnetic field.

15. Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.3, Page – 988
Example II:
(a) When the magnet is moved toward the stationary conducting loop, a current
is induced in the direction shown. (b) According to right hand rule this induced
current produces its own magnetic flux that is directed to the left and so
counteracts the increasing external flux to the right.

16. Reference: Physics II by Robert Resnick and David Halliday, Topic – 31.3, Page – 988
(c) When the magnet is moved away from the stationary conducting loop, a
current is induced in the direction shown. (d) According to right hand rule this
induced current produces a magnetic flux that is directed to the right and so
counteracts the decreasing external flux to the right.

18. Later
Reference:
Law