A magnetic flux through a stationary loop with a resistance `R` varies during the time interval `tau` as `phi=at(tau-t)`. Find the amount of the generated in the loop during that time

Explanation

Given that `phi = at(T-t)`, induced emf, `E = (d phi)/(dt)`
`= (d)/(dt)[at(T-t)], = at(0-1) + a(T-1), = a(T-2t)`
So, induced emf is alos a function of time Heat generated
`H = underset(0)overset(T)int(E^(2))/(R )dt` , `= (a^(2))/(R )underset(0)overset(T)int(T-2t)dt , = (a^(2)T^(3))/(3R)`