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Question:

Two wires A and B are carrying currents I1 and I2 as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are:

x=±(I1d/I1−I2)

x=I2/(I1+I2)d and x=I1/(I1−I2)d

x=I1/(I1+I2)d and x=I2/(I1−I2)d

x=I1/(I1−I2)d and x=I2/(I1−I2)d

Solution:

Correct option is B.
x=±(I1d/I1−I2)
Net force on wire carrying current I per unit length is μ0I1I/2πx + μ0I2I/2π(d−x) = 0
I1/x = I2/(d−x) ⇒ x = I1d/(I1−I2)