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A rectangular loop of wire ABCD is kept ...

A rectangular loop of wire ABCD is kept close to an infinitely long wire carring a current I (t) `= I_(0) (1 = t//T)` for `0 le t le` and I (0) for t gt T, Fig. Find the total charges passing through a given point in the loop, in time T. resistance of the loop is R

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In Fig. XY is an infinitely long wire carruying current
`I (t) = I_(0) (1 - t//T)` for `0 le t le T`
If I (t) is current induced in the loop, then
`I (t) = (d phi // dt)/(R ) = (dQ)/(dt)`
Integrating both sides, we get `Q (t_(1)) = Q (t_(2)) = (1)/(R ) [phi (t_(1)) - phi (t_(2))]`
using (i) of Q .25 , `phi (t_(1)) = L_(1) (mu_(0))/(2 pi) int_(x)^(L_(2) + x) (dx')/(x') I (t_(1)) = (mu_(0) L_(1))/(2 pi) I (t_(1)) log_(e) ((L_(2) + x)/(x))`
`:.` The magnitude of charge would be `Q = (mu_(0) L_(1))/(2 pi) log_(e) ((L_(1) + x)/(x)) [I_(1) - 0] = (mu_(0) L_(1) I_(1))/(2 pi) log_(e) ((L_(2) + x)/(x))`
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