Question

Two parallel long wires A and B carry currents $i_1$ and $i_2 (< i_1)$. 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 reverse the field becomes $30\, \mu T$. The ratio $i_1/i_2$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is B

$\frac{\mu_{0}}{4\pi} \frac{2i_{1}}{r}-\frac{\mu_{0}}{4\pi} \frac{2i_{2}}{r}=10 \mu T$ $\frac{\mu _{0}}{4\pi }\frac{2i_{1}}{r}+\frac{\mu _{0}}{4\pi } \frac{2i_{2}}{r}=30 \mu T$ On solving $i_{1} = 20 A and i_{2} = 10 A. ? i_{1}/i_{2} = 2$