A magentic flux through a statinary loop with a resistance `R` varies during the tiem interval `tau` as `Phi = at (tau - t)`. Find the amount of heat generated in the loop during that time. The inductance of the loop is to be neglected.

Explanation

The amount of heat generated in the loop during a small time interval `dl`,
`d Q = xi^(2)//R dt`, but `xi = - (d Phi)/(dt) = 2 at-a tau`,
So, `d Q = ((2 at - a tau)^(2))/(R) dt`
and hence, the amoung of heat, generated in the loop during the time interval 0 to `tau`.
`Q = int_(0)^(tau) ((2at - a tau)^(2))/(R) dt = (1)/(3) (a^(2) tau^(3))/(R)`