Definition:

Electromagnetic induction is the phenomenon in which a changing magnetic field induces an electromotive force (EMF) in a conductor.

• Discovered by Michael Faraday in 1831.

• Later formulated mathematically by Joseph Henry (independently).

📌 Faraday’s Law of Electromagnetic Induction

The induced EMF in a circuit is proportional to the rate of change of magnetic flux through the circuit.

E=−dΦBdt\mathcal{E} = - \frac{d\Phi_B}{dt}E=−dtdΦB

Where:

• E\mathcal{E}E = induced EMF (V)

• ΦB=B⋅A⋅cos⁡θ\Phi_B = B \cdot A \cdot \cos\thetaΦB=B⋅A⋅cosθ = magnetic flux (Wb)

• BBB = magnetic field, AAA = area, θ\thetaθ = angle between B and normal to the loop

Negative sign → Lenz’s Law (opposition to change in flux).

📌 Lenz’s Law

The direction of induced current (or EMF) opposes the change in magnetic flux that produced it.

• This is a consequence of conservation of energy.

• Example: If flux increases → induced current creates opposite field to resist increase.

🔹 Motional EMF

• When a conductor of length lll moves with velocity vvv perpendicular to magnetic field BBB: