Question

Two magnetic monopoles are kept apart by certain distance and magnetic force acting is '$F$'. If pole strength of one pole is increased by $100$% and another is increased by $100$%, by what percentage distance between them be increased so that magnetic force acting will remain to be '$F$'.

Answer 1

As magnetic force between two non poles will be directly proportion to pole strength and inversely proportional to square of distance between them, so

$F=K\frac{m_1{m}_2}{r^2}\to \left(1\right)$

now $m_1^{{}^{\prime }}=2m_1$ (100 % increase)

$F=K\frac{m_1{m}_2}{r^2}\to \left(1\right)$

now $m_1^{{}^{\prime }}=2m_1$

$m_2^{{}^{\prime }}=2m_2$

Distance between poles$=r^{\prime }$

$\therefore F=K\frac{\left(2m_1\right)\left(2m_2\right)}{(r^{\prime }{)}^2}\to \left(2\right)$

dividing (1) and (2) , we get

$\frac{1}{1}=\frac{(r^{{}^{\prime }}{)}^2\ast 1}{r^2\ast 4}$

$\therefore (r^{{}^{\prime }}{)}^2=4r^2$

$\therefore r^{\prime }=2r$

Here distance should be increased by 100%