Two infinitely long parallel wires carry currents of magnitude`I_(1)` and `I_(2)` and are at a distance 4 cm apart. The magnitude of the net magnetic field is found to reach a non-zero minimum values between the two wires and 1 cm away from the first wire. The ratio of the two currents and their mutual direction is

Options

A. `(I_(2))/(I_(1))` = 9 , anti-parallel
B. `(I_(2))/(I_(1))= 9` , parallel
C. `(I_(2))/(I_(1)) = 3` , anti-parallel
D. `(I_(2))/(I_(1)) = 3` , parallel

Answer

A

Explanation

`B = (mu_(0) I_(1))/(2pi x) + (mu_(0) I_(2))/(2pi (4 - x)) implies (dB)/(dx) = 0 implies (I_(1))/(x^(2)) = (I_(2))/((4 - x)^(2))`
So , `x = 1 implies (I_(2))/(I_(1)) = 9`