Question

The ratio of magnetic fields on the axial line of a long magnet at distances of $10cm$ and $20cm$ is $12.5:1$. The length of the magnet is:

• A. $5cm$
• B. $10cm$
• C. $10m$
• D. $15m$

Answer 1

Answer: (B)

$10cm$

Magnetic field at an axial point
$B_{axial}=\frac{{\mu }_0}{4\pi }\frac{2Md}{(d^2-l^2{)}^2}$
wherer $M$ is the magnetic moment, d is the distance of the point from center of the magnet and $2l$ is the length of the magnet.
Substituting the values provided,
$\frac{B_1}{B_2}=\frac{d_1}{d_2}\frac{d_2^2-l^2}{(d_1^2-l^2{)}^2}$
$\Rightarrow \frac{12.5}{1}=\frac{10}{20}\times (\frac{{20}^2-l^2}{{10}^2-l^2}{)}^2$
$\Rightarrow 5\times ({10}^2-l^2)=({20}^2-l^2)$
$\Rightarrow l=5$
$\Rightarrow 2l=10$