Question

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

Answer 1

The work done by us in moving the cross wire converts into electrical energy. So the work done is given byW = FSSubstitute (1) W = $F _{ s }$ = BIls -----»(2)$\triangle$$\phi$ = Bls ------ > (3)From (2) and (3)W = ($\triangle$$\phi$) ILet us divide both sides by AtW/$\triangle$t = I $\triangle$$\phi$ /$\triangle$t------> (4)$\Sigma $ = $\triangle$$\phi$ /$\triangle$tElectric power, P = $\Sigma $I ----->(5)Electric power, P = I ($\triangle$$\phi$ /$\triangle$t)Divide (2) by $\triangle$tW / $\triangle$t = Fs / $\triangle$t = BIls /$\triangle$t -----> (6)Here s / $\triangle$t gives the speed of the crosswire, let it be v.Electric powerP = W / $\triangle$t = Fv = BIlv ----->(7)Power is also given as force times velocity.From (5) and (7), $\Sigma $I = BIlv

Answer 2

A current will set up in the circuit only when there is an EMF in the circuit. Let this EMF be e. According to principle of conservation of energy this electric energy must come from the work that we have done in moving the cross wire. Here s / $\triangle$t gives the speed of the cross wire, let it be v