Physics - Magnetism Question with Solution | TestHub

When the currents are in the same direction then the magnetic field

$B=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{2}{d} \left[i_1-i_2\right]$

$6\times {10}^{-6}= \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{2}{d} \left[i_1-i_2\right] \dots \left(\mathrm{i}\right)$

When the currents are in the reversed direction then the magnetic field

$B_2=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{2}{d} \left[i_1-(-i_2)\right]$

or$B_2=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{2}{d} \left[i_1+i_2\right]$

or$3\times {10}^{-5}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{2}{d}\left[i_1+i_2\right] \dots \left(\mathrm{i}\mathrm{i}\right)$

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$4i_1=6i_2$

$\frac{i_1}{i_2}=\frac{6}{4}$

$\frac{i_1}{i_2}=\frac{3}{2}$