Question

$AB$ and $CD$ are long straight conductor, distance $d$ apart, carrying a current $I$. The magnetic field at the midpoint of $BC$ is

• A. $\frac{-{\mu }_{0}I}{2\pi d}\hat{k}$
• B. $\frac{-{\mu }_{0}I}{\pi d}\hat{k}$
• C. $\frac{-{\mu }_{0}I}{4\pi d}\hat{k}$
• D. $\frac{-{\mu }_{0}I}{8\pi d}\hat{k}$

Answer 1

Answer: (B)

$\frac{-{\mu }_{0}I}{\pi d}\hat{k}$

The field at the midpoint of $BC$ due to $AB$ is $(-\frac{{\mu }_0}{4\pi }.\frac{i}{d/2}\hat{k})$ and the same is due to $CD$.

Therefore the total field is $[-\left(\frac{{\mu }_{0}i}{\pi d}\right)\hat{k}]$