Q. The distance of two points on the axis of a magnet from its centre is $10\ cm$ and $20\ cm$ respectively. The ratio of magnetic intensity at these points is $12.5\ :1$. The length of the magnet will be
A) 5 $cm$
B) 25 $cm$
C) 10 $cm$
D) 20 $cm$
Explanation
(c) $\frac{B_{1}}{B_{2}} = \frac{d_{1}}{d_{2}}\left( \frac{d_{2}^{2} - l^{2}}{d_{1}^{2} - l^{2}} \right)^{2} \Rightarrow \frac{12.5}{1} = \frac{10}{20}\left( \frac{400 - l^{2}}{100 - l^{2}} \right)^{2}$
$\Rightarrow l = 5\ cm$
Hence length of magnet $= 2l = 10\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.