Question

Two parallel, long wires carry currents $i_1$ and $i_2$ with $i_1>i_2.$ When the currents are in the same direction, the magnetic field at a point midway between the wires is $10\mu T$. If the direction of $i_2$ is reversed, then the field becomes $30\mu T$. The ratio $\frac{i_1}{i_2}$ is:

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

Let the point $P$ be at a distance $r$ from each of the wires.
Magnetic field at $P:B=\frac{{\mu }_0}{2\pi r}(i_1-i_2)=10$ when $i_1\parallel i_2$

Magnetic field at $P:B=\frac{{\mu }_0}{2\pi r}(i_1+i_2)=30$ when $i_1$ is anti-parallel to $i_2$

From the above 2 equations
$\frac{i_1+i_2}{i_1-i_2}=\frac{30}{10}$

$\Rightarrow \frac{2i_1}{2i_2}=\frac{30+10}{30-10}=2$

$\Rightarrow \frac{i_1}{i_2}=2$