Question

The force between two magnetic poles reduces to $aN$, if distance between them is increased to $n$ times and it increases to $bN$ if the distance between them is $1/n^{th}$ the original value. Then $a:b$ is :

• A. $1:n^2$
• B. $n^2$:1
• C. $n^4$:1
• D. $1:n^4$

Answer 1

The correct option is D $1:n^4$

Force between the two poles follows inversely square law:

$F=\frac{{\mu }_0{m}_1{m}_2}{4\pi d^2}$

$F_{1}aN=\frac{{\mu }_0{m}_1{m}_2}{4\pi (nd{)}^2}$

$F_{2}bN=\frac{{\mu }_0{m}_1{m}_2}{4\pi (\frac{d}{n}{)}^2}$

$\frac{F_1}{F_2}=\frac{a}{b}=\frac{1/n^2}{\frac{1}{1/n^2}}$

$\therefore a:b=1:n^4$