Derive Faraday's law of induction from law of conservation of energy.

We know that Force applied on a wire in magnetic field is given by

F = BIL

Where;

B = Magnetic field;

I = Current in the wire;

L = Length of the wire;

Also, Work = Force × Distance;

⇒ W = FS.

⇒ W = BILS. (1) (∵ F = BIL).

When the wire moves in the magnetic field the decrease in flux (Φ) is

ΔΦ = BA

⇒ ΔΦ = BLS (2) (∵ Area = Length(L) x Breadth(S) )

From (1) W = BILS

W = (BLS)I.

From (2) ΔΦ = BLS

⇒ W = (ΔΦ)I .

Dividing Both sides by Δt.

⇒ (∵ )

⇒ (3)

∵

⇒ ( From (3) ).

Also Electrical Power (p) = E x I (4)

Where I = current;

E=EMF( Electromagnetic Force);

The Electrical power generated is used as the mechanical energy to move the wire. (Law of energy conservation)

⇒ EI = BILV (From (3) and (4) )

⇒ E = BLV.

∴ Induced EMF is BLV.