The magnetic flux through a stationary loop with resistance R varies during interval of time ? as Φ=at(T−t). The heat generated during this time neglecting the inductance of loop will be

Given that, Φ=at(T−t)=atT−at2∴e=dΦdt=aT−2at=a(T−2t)Let heat generated in time dt be dH ThendH=i2Rdt=e2R2×Rdt=e2dtRTotal heat generated can be obtained by integrating above expression, i,e.,∫0T dH=∫0T e2dtRH=1R∫0T e2dt=1R∫0T a2(T−2t)2dt=a2RT2t+4t33−2t2T0T=a2RT3+4T33−2T3=a2T33R