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:

Options

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`

Answer

B

Explanation

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 of B. In these cases,
`B_(1)=B_(2)implies(mu_(0)I_(1))/(2pix)=(mu_(0)I_(2))/(2pi(d+x))` or `(mu_(0)I_(1))/(2pix)=(mu_(0)I_(2))/((x-d))impliesx=(I_(1)d)/(I_(2)-I_(1))` or `x=(I_(1)d)/((I_(1)-I_(2))`