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.

contexto.120

3 years ago

If the instantaneous current is t, then

I(t) = 1/R d/dt I(t)

If q is the charge that passes during time t,

dQ/dt = I(t)

1/R d/dt = dQ/dt

When we integrate the equation, we obtain

Q = 0L1L2/2R log (L2 + x/x)