A square loop of side length d has a capacitor of capacitance C and the resistance of the loop is R. In the plane of the loop there is a long straight current carrying wire having current I. The distance of the straight wire from the loop is d as shown in figure. The current in the straight wire is made to grow with time as `I = alpha t` where `alpha = 2 As^(-1)`. Neglect self inductance of the loop.
(a) Find the charge on the capacitor as a function of time (t).
(b) Find the heat generated in the loop as a function of time.
(c) Who supplies energy for heat dissipation?

Answer

(a) `q=epsilonC(1-e^(-t//RC))`
(b) `H=(epsilon^(2)C)/(2)(1-e^(-(2t)/(RC)))` where `epsilon=(mu_(0)alpha.dl n2)/(2pi)`