The ratio of magnetic inductions on the axial line of a bar magnet at distances 10cm and 15cm from the center of the magnet are in the ratio 5.8: 1. The distance between the two poles of the magnet is

$For long bar magnet, B_{axial} = \frac{{\mu }_o}{4\pi }\frac{2Md}{{(d^2-l^2)}^2}$

$\Rightarrow B\propto \frac{d}{{(d^2-l^2)}^2}$

$\Rightarrow \frac{5.8}{1}=\frac{10}{15}{\left[\frac{{15}^2-l^2}{{10}^2-l^2}\right]}^2$

$\Rightarrow 8.7 {({10}^2-l^2)}^2= {({15}^2-l^2)}^2 \Rightarrow 2.95 (100-l^2) = (225-l^2)$

$$\begin{gathered} \Rightarrow l^2 = \frac{295-225}{2.95-1}=\frac{70}{1.95}\simeq 36 \\ \Rightarrow l=6 \end{gathered}$$

$\Rightarrow Dis\tan ce between two poles=2l=12cm$