Question

Three similar magnetic south poles, each of strength $10\text{Am}$ are placed at the corners of an equilateral triangle of side $20\text{cm}$. The magnetic force on one of the pole is:

• A. $0.25\times {10}^{-3}\text{N}$
• B. $2\times {10}^{-3}\text{N}$
• C. $2.5\sqrt{3}\times {10}^{-4}\text{N}$
• D. $5\times {10}^{-3}\text{N}$

Answer 1

The correct option is C $2.5\sqrt{3}\times {10}^{-4}\text{N}$

Given,

Magnetic strength of poles,

$m_1=m_2=m_3=10\text{Am}$


Let,

$F_{12}=$Repulsive force on the pole $2$ due to pole $1$,

$F_{32}=$Repulsive force on the pole $2$ due to pole $3$,

Net force on the pole $2$ is,
$F_{net}=\sqrt{{F_{12}}^2+{F_{32}}^2+2F_{12}{F}_{32}\cos {60}^{\circ }}$

As, $F_{12}=F_{32}=F$(Assume)

$\Rightarrow F_{net}=\sqrt{F^2+F^2+2F^2\times \frac{1}{2}}$

$\Rightarrow F_{net}=\sqrt{3F}$

As, $F=\frac{{\mu }_0}{4\pi }\frac{m_1{m}_2}{r^2}={10}^{-7}\times \frac{10\times 10}{0.2\times 0.2}=0.25\times {10}^{-3}\text{N}$

$\therefore F_{net}=2.5\sqrt{3}\times {10}^{-4}\text{N}$

Hence, option $\left(D\right)$ is the correct answer.