Question

The intensity of magnetic field at point X on the axis of a small magnet is equal to the field intensity
at another point y on its equatorial axis. The ratio of X and Y from the centre of the magnet will be

• A. $2^{-3}$
• B. $(2{)}^{-1/3}$
• C. $2^3$
• D. $2^{1/3}$

Answer 1

The correct option is D $2^{1/3}$

If $d_1$ is the distance of point X on axial line and $d_2$ is distance of point Y on equatorial line, then
$B_1=\frac{{\mu }_0}{4\pi }\frac{2M}{d_1^3},B_2=\frac{{\mu }_0}{4\pi }\frac{M}{d_2^3}As{B}_1=B_2\therefore \frac{{\mu }_0}{4\pi }\frac{2M}{d_1^3}=\frac{{\mu }_0}{4\pi }\frac{2M}{d_2^3}{d}_1^3=2d_2^3;\frac{d_1}{d_2}=2^{1/3}$