Question

Two north poles each of pole strength m and a south pole of pole strength m are placed at the three corners of an equilateral triangle of side a. The intensity of magnetic induction field strength at the centroid of the triangle is :

• A. $\frac{{\mu }_0}{4\pi }\frac{m}{a^2}$
• B. $\frac{{\mu }_0}{4\pi }\frac{6m}{a^2}$
• C. $\frac{{\mu }_0}{4\pi }\frac{9m}{a^2}$
• D. $\frac{{\mu }_0}{4\pi }\frac{m}{2a^2}$

Answer 1

The correct option is B $\frac{{\mu }_0}{4\pi }\frac{6m}{a^2}$

$H_{horizontal}=H_{1}cos{30}^0+H_{2}cos{30}^0$

$H_{Vertical}=H_{1}sin{30}^0-H_{2}sin{30}^0-H_3$

$|H_1|=|H_2|=|H_3|$

therefore , $H_{Horizontal}=\frac{2H\sqrt{3}}{2}=H\sqrt{3}$

and , $H_{Vertical}=-H$

therefore, $H_{Net}=\sqrt{(\sqrt{3}H{)}^2+H^2}=2H$

And, $H=\frac{\mu m}{4\pi r^2}$ where, $r=\frac{a}{\sqrt{3}}$

therefore, $H_{Net}=\frac{\mu }{4\pi }\frac{6m}{a^2}$