A rectangular loop of sides 8 cm and 2 cm with a small cut is stationary in a uniform magnetic field directed normal to the loop. The magneic field is reduced form its initial value of 0.3 T at the rate of 0.2 T `s^(-1)`. If the cut is joined and the loop has a resistance of `1.6 Omega`, how much power is dissipated by the loop as heat ?

Explanation

At instant t, let the radius of the loop be r. Therefore, magnetic flux linked with the loop at this instant, `phi = pi r^(2) B`
`(d phi)/(dt) = 2 pi r B (dr)/(dt)`
When `r = 2 xx 10^(-2) m`
and `(dr)/(dt) = 10^(-3) m//s`,
`e = (d phi)/(dt) = 2 xx (22)/(7) (2 xx 10^(-2)) (0.02) xx 10^(-3)`
`= 2.5 xx 10^(-6) V = 2.5 mu V`