Question

A current of $1$ ampere is following in the sides of an equilateral $△$ of side $2m$. Find the magnetic field at the centroid of the $△$.

Answer 1

$\tan {60}^0=\frac{1}{x}$

$x=\frac{1}{\sqrt{3}}$

$\overrightarrow{B}=\frac{\mu oi}{4\pi x}.\left(\sin {60}^0+\sin {60}^0\right)\times 3$

$\Rightarrow \overrightarrow{B}=\frac{\mu o\times 1}{4\pi \left(\frac{1}{\sqrt{3}}\right)}\times \sqrt{3}\times 3$

$=3\frac{\mu o}{4\pi }\times 3=\frac{9\mu o}{4\pi }=9\times {10}^{-1}T$

$\therefore$ Magnetic field at centroid $9\times {10}^{-1}T.$