Question

A regular hexagon of side length $a$ carries current $I$. Magnitude of magnetic field at its center is

• A. $\frac{\sqrt{3}{\mu }_{0}I}{\pi a}$
• B. $\frac{\sqrt{3}}{2}\frac{{\mu }_{0}I}{\pi a}$
• C. $\frac{3}{2}\frac{{\mu }_{0}I}{\pi a}$
• D. $\frac{3{\mu }_{0}I}{\pi a}$

Answer 1

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


Field at 0 due to side AB is $B=\frac{{\mu }_0}{4\pi }\frac{I}{l}(\sin \theta +\sin \theta )[\theta ={30}^{\circ }]$
$l=a\cos \theta =\frac{\sqrt{3}a}{2}$

$\Rightarrow B=\frac{{\mu }_0}{4\pi }\frac{I\times 2}{\sqrt{3}a}\because B_{net}=6B$

$\Rightarrow B_{net}=\frac{{\mu }_0}{4\pi }\frac{I\times 2\times 6}{\sqrt{3}a}=\sqrt{3}\frac{{\mu }_{0}I}{\pi a}$