A rectangular loop of wire ABCD is kept

Question:

 A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current II ( ) t = o (1– /t T ) for 0 ≤ ≤ t T and I (0) = 0 for t > T. Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

Solution:

If t is the instantaneous current then,

I(t) = 1/R dϕ/dt

If q is the charge passing in time t

I(t) = dQ/dt

dQ/dt = 1/R dϕ/dt

Integrating the equation we get,

Q = μ0L1L2/2πR log (L2 + x/x)

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