question_answer

Two long parallel wires carry currents \[{{i}_{1}}\] and \[{{i}_{2}}\] such that\[{{i}_{1}}>{{i}_{2}}\]. When the currents are in the same direction, the magnetic field at a point midway between the wires is\[6\times {{10}^{-6}}T\]. If the direction of ii is reversed, the field becomes\[3\times {{10}^{-5}}T\]. The ratio of \[{{i}_{1}}/{{i}_{2}}\] is -

A) 1/2                   

B)        2

C) 2/3                   

D)        3/2

Correct Answer: D

Solution :

[d] \[\frac{{{B}_{1}}}{{{B}_{2}}}=\frac{\frac{{{\mu }_{0}}}{2\pi }\left( \frac{{{i}_{1}}}{d}-\frac{{{i}_{2}}}{d} \right)}{\frac{{{\mu }_{0}}}{2\pi }\left( \frac{{{i}_{1}}}{d}+\frac{{{i}_{2}}}{d} \right)}\]