Question

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

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

Answer 1

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

$\begin{array}{c}\frac{{\mu }_{0}i}{4\pi \left(\frac{L}{4}\right)}\left(2\sin \theta \right)\\ =\frac{2{\mu }_{0}i}{L\pi }\left[\frac{L/2}{\sqrt{5}L/4}\right]\\ =\frac{4{\mu }_{0}i}{\sqrt{5}L\pi }\\ Hence,\\ optionAiscorrectanswer.\end{array}$