A current of I ampere is flowing in the sides of an equilateral triangle of side ' $a$ '. The magnet

Question

A current of I ampere is flowing in the sides of an equilateral triangle of side ' $a$ '. The magnetic field at the centroid of the triangle is\

Professor PC Thomas Classes · Answer

The magnetic field at O due to current through all the three sides of a triangle will be\ $B=3 B_{1}=3 \frac{\mu_{0} I}{4 \pi r}\left(\sin 	heta_{1}+\sin 	heta_{2}ight)$\ $	heta_{1}=	heta_{2}=60^{\circ}$\ Here $\mathrm{r}=\mathrm{OD}$\ $	an 60=\frac{B D}{O D} \frac{d / 2}{O D} \quad O D=\frac{a}{2 	an 60}=\frac{a}{2 \sqrt{3}}$\ $B=3 \frac{\mu_{0} i}{4 \pi a / 2 \sqrt{3}} 	imes(\sin 60+\sin 60)$\ $\frac{18 \mu_{0} \mathrm{i}}{4 \pi \mathrm{a}}$