Question

A current $l$ is flowing in a straight conductor of length $L$. The magnetic induction at a point on its axis at a distance $\frac{L}{4}$ from its centre will be

• A. $zero$
• B. $\frac{{\mu }_{0}l}{2\pi L}$
• C. $\frac{{\mu }_{0}l}{\sqrt{2}L}$
• D. $\frac{4{\mu }_{0}l}{\sqrt{5}\pi L}$

Answer 1

The correct option is D $\frac{4{\mu }_{0}l}{\sqrt{5}\pi L}$

$B=\frac{{\mu }_{0}i}{4\pi d}\left(\sin {\varphi }_1+\sin {\varphi }_2\right)$

$=\frac{{\mu }_{0}i}{4\pi \left(\frac{L}{4}\right)}\left(\frac{2}{\sqrt{5}}+\frac{2}{\sqrt{5}}\right)$

$=\frac{4{\mu }_{0}i}{\sqrt{5}\pi L}$

Hence,

option $\left(D\right)$ is correct answer.