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

Answer: (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 $i_1=20Aand{i}_2=10A.\therefore i_1/i_2=2$