Question

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 $i_2$ is reversed, the field becomes $3\times {10}^{-5}T.$ The ratio $\frac{i_1}{i_2}$ is

• A. $\frac{1}{2}$
• B. 2
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$
• E. $\frac{1}{5}$

Answer 1

Answer: (D)

When the currents are in the same direction then magnetic field
$B=\frac{{\mu }_0}{4\pi }\times \frac{1}{d}[{i_{}}_1-i_2]$
$6\times {10}^{-6}=\frac{{\mu }_0}{4\pi }\times \frac{2}{d}[i_1-i_2]$ ...(i)
When the currents are in the reversed direction then magnetic field
$B_2=\frac{{\mu }_0}{4\pi }\times \frac{2}{d}[i_1-(-i_2)]$
Or $B_2=\frac{{\mu }_0}{4\pi }\times \frac{2}{d}[i_1+i_2]$
or $3\times {10}^{-5}=\frac{{\mu }_0}{4\pi }\times \frac{2}{d}[i_1+i_2]$ ...(ii) Dividing Eq. (i) by Eq. (ii)
$\frac{i_1-i_2}{i_1+i_2}=\frac{6\times {10}^{-6}}{3\times {10}^{-5}}$
Or $\frac{i_1-i_2}{i_1+i_2}=\frac{2}{10}$
Or $5i_1-5i_2=i_1+i_2$
Or $4i_1=6i_2$
Or $\frac{i_1}{i_2}=\frac{6}{4}$
Or $\frac{i_1}{i_2}=\frac{3}{2}$