Question

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

Answer 1

1st case:

$B=B_1-B_2$

$10\times {10}^{-3}=\frac{{\mu }_0{i}_1}{2\pi r}-\frac{{\mu }_0{i}_2}{2\pi r}$

$\frac{{\mu }_0}{2\pi r}(i_1-i_2)=0.01$

2nd case:

$B=B_1+B_2$

$30\times {10}^{-3}=\frac{{\mu }_0{i}_1}{2\pi r}+\frac{{\mu }_0{i}_2}{2\pi r}$

$\frac{{\mu }_0}{2\pi r}(i_1+i_2)=0.03$

$\therefore \frac{i_1-i_2}{i_1+i_2}=3$

$i_1-i_2=3i_1+3i_2$

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