Question

A closed circuit is in the form of a regular hexagon of side a. If the circuit carries current I, What is magnetic induction at the cetre of the hexagon?

• A. $\frac{\sqrt{3}{\mu }_{0}i}{\pi a}$
• B. $\frac{\sqrt{3}{\mu }_{0}i}{\pi a}$
• C. zero
• D. None

Answer 1

The correct option is A $\frac{\sqrt{3}{\mu }_{0}i}{\pi a}$

$\alpha =\beta B=6\left[\frac{{\mu }_i}{4\pi r}\right(sin\alpha +sin\beta \left)\right]=6\left[\frac{{\mu }_{o}i}{4\pi r}2sin30\right]=\frac{6{\mu }_{0}i\times 2\times \frac{1}{2}}{2\pi \sqrt{3}a}here,r=\sqrt{a^2-\frac{a^2}{4}}=\sqrt{3}\frac{a}{2}$
$=\frac{\sqrt{3}{\mu }_{0}i}{\pi a}$