Figure showns a fixed square frame of wire having a total resistance `r` placed coplanarly with a long staight wire.The wire carries a current `i` given by `i=i_(0)cos (2pil//T)`.Find (a) the flux of the magnetic field through the square frame (b)the `emf` induced in the frame and (c) the heat developed in the frame in the time interval `0` to `10 T`.

Answer

A, B, C

Explanation

(a)`phi=intB.ds`
`=underset(b)overset(a+b)int(mu_(0)i)/(2pir)xxadr=(mu_(0)ia)/(2pi)ln((a+b)/b)`
(b)`epsilon=-(dphi)/(dt)=(mu_(0)ai_(0))/(2pi)(2pi)/T sin (2pit)/T ln ((a+b)/b)`
(c)`Q=underset(0)overset(10T)int epsilon^(2)/rdt=((5mu_(0)^(2)i_(0)^(2)a^(2))/(Tr))[ln((a+b)/b)]^(2)`