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Two wires A and B are carrying currents ...

Two wires A and B are carrying currents `I_(1)` & `I_(2)` as shown in the figure. The separation between them is d. A third wire C carrying a current I is to kept parallel to them at a distance x from A such that the net forces acting on it is zero. The possible values of x are:

A

`x=(I_(1)/(I_(1)+I_(2))d)` and `x = (I_(2)/(I_(1)-I_(2)))d`

B

`x=+-(I_(1)/(I_(1)-I_(2)))d`

C

`x=(I_(1)/(I_(1)-I_(2)))d` and `x =I_(2)/(I_(1)+I_(2))d`

D

`x=(I_(2)/(I_(1)-I_(2)))d` and `x =I_(2)/(I_(1)-I_(2))d`

Text Solution

Verified by Experts

The correct Answer is:
B
Force on wire C is zero when net magnetic field due to wires A and B is zero.
This is possible only when wire C is either left of A or right B of B.
`B_(1) = B_(2) rArr (mu_(0)I_(1))/(2pi x) =(mu_(0)I_(2))/(2pi(d+x))` or `(mu_(0)I_(1))/(2pix) =(mu_(0)I_(2))/(x-d) rArr x=(I_(1)d)/(I_(2)-I_(1))` or `x=(I_(1)d)/(I_(1)-I_(2))`
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