Question

Two magnetic monopoles are kept apart by a distance '$d$'. The magnetic force acting on each pole is '$F$'. How much percentage must the distance between the magnetic poles be changed so that the magnetic force acting on each pole be $4F$.

• A. Decreases by $50$%
• B. Decreases by $20$%
• C. Increased by $50$%
• D. Increased by $20$%

Answer 1

The correct option is A Decreases by $50$%

Given, magnetic field at a pole due to one pole at d distance from another pole=F and

$\overrightarrow{B}=\frac{{\mu }_0\left(2M\right)}{4\pi d^2}$

When $B_{\text{new}}=4F$

$\therefore \frac{B_{\text{new}}}{B}=4$

$⟹\frac{{\mu }_0\left(2M\right)}{4\pi d^2}\times \frac{4\pi d^2}{{\mu }_0\left(2m\right)}=4$

$⟹d^2=4d^2$

$⟹d^1=\frac{d}{2}$

Thus decreases by 50%.