Q. Two parallel long wires $A\ and\ B$ carry currents $i_{1}\ and\ i_{2}\ \left( < i_{1} \right).\ $When $i_{1}\ and\ i_{2}$ are in the same direction, the magnetic field at a point mid way between the wires is 10 $\mu$ T. If $i_{2}$ is reversed, the field becomes 30 $\mu$ T. The ratio $i_{1}/i_{2}$ is
A) 1
B) 2
C) 3
D) 4
Explanation
(b) $\frac{\mu_{0}i}{4\pi}\frac{2i_{1}}{r} - \frac{\mu_{0}}{4\pi}\frac{2i_{2}}{r} = 10\mu\ $T
$\frac{\mu_{0}i}{4\pi}\frac{2i_{1}}{r} + \frac{\mu_{0}}{4\pi}\frac{2i_{2}}{r} = 30\ \pi\ $T
On solving $i_{1} = 20\ A\ and\ i_{2} = 10\ A,\ So,\ i_{1}/i_{2}$ = 2
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.