I am Michael Faraday – Discovery (1831): Electromagnetic Induction.
When a magnet is moved toward or away from a coil, an induced current is generated in the coil.
An induced emf arises due to the change in magnetic flux through the coil.
The current is induced when the magnetic field through a conducting loop changes.
The cause: motion of the magnet (approach or retreat) changes the magnetic flux through the coil.
Independently, Henry investigated induced currents by changing the field through a coil.

Useful info: Electromagnet – when current flows in a coil, it becomes an electromagnet.
Using the right-hand grip rule, we determine the field direction.
Thumb points to the direction of the field inside the coil (points to North Pole).
Note: North pole – current counterclockwise; South pole – current clockwise (when viewed from the pole side).

Electromagnetic induction and Faraday's experiment:
Moving a conductor in an external magnetic field generates an electric current inside the conductor.
Approach of magnet to coil → opposing field to reduce flux change.
Retreat of magnet → similar field to reduce flux change.
Faraday showed that the average induced emf equals the time rate of change of magnetic flux.
For a coil with N turns: \[ \mathcal{E} = -N \frac{d\Phi_B}{dt} \]

Test yourself: When N-pole magnet approaches the coil, induced current direction?

What is the direction of current and the pole facing you?

When S-pole magnet approaches the coil, induced current direction?

When N-pole magnet moves away from the coil, induced current direction?

When S-pole magnet moves away from the coil, induced current direction?

Two coils: Coil A connected to battery & resistor, coil B connected to galvanometer.

When switch is closed, determine the poles of coil A.

After closing circuit A, determine the poles of coil B.

When resistance in circuit A is increased (while closed), determine the poles of coil B.

A circular coil of area \[A=0.1 m^2\] is placed in a uniform magnetic field \[B=0.3 T\] as shown. Calculate the flux in the following cases:

Induced EMF due to changing magnetic field

\[ \mathcal{E} = - N A \cos\theta \frac{dB}{dt} \]

Induced EMF due to changing area

\[ \mathcal{E} = - B \cos\theta \frac{dA}{dt} \]

Induced EMF due to changing angle (rotation)

\[ \mathcal{E} = A B \sin\theta \frac{d\theta}{dt} = A B \omega \sin\theta \]

I am Heinrich Lenz

When approaching a magnet to a coil (increasing flux), the induced current creates a magnetic field opposing the change.
When retreating (decreasing flux), the induced current creates a field in the same direction as the change.
This is Lenz's law: the induced emf opposes the change in flux.

\[ \mathcal{E} = - \frac{d\Phi_B}{dt} \]

The negative sign indicates opposition to the cause.

Which of the following produces an induced current clockwise (viewed from above)?

Metal detector: It consists of a transmitter coil and a receiver coil. The transmitter coil is connected to an AC source, producing a changing magnetic field that induces a current in the receiver coil. When a metal object passes near, it acts like a secondary coil, and by Lenz's law it generates an opposing field that reduces the receiver's field, triggering a signal.