# Prove that electromagnetic induction is conservation of energy in nature?

Verification of conservation of Energy:- If the resistance of the expanding loop is assumed as R, then the current flowing in the loop is $i=frac{varepsilon }{R}=frac{BLV}{R}$

The rate of E.D by the ext.agency in moving the conducting rod with a constant velocity (V) against the magnetic force FB = ILBis given by

P = (ILB)V

= $frac{{{B}^{2}}{{L}^{2}}{{V}^{2}}}{R}$

=$frac{{{varepsilon }^{2}}}{R}$ = power dissipated heat in overcoming the resistance ‘R

As the rod is moving on the parallel rails smoothly

⸫ mechanical energy is converted into electrical energy & which is dissipated as heat to overcome the resistance of the loop.