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 distance of X and Y from the center of the magnet will be;

• A. 2⁻³
• B. (2)⁻¹/³
• C. 2³
• D. 2¹/³

Answer 1

Answer: (B)

(2)⁻¹/³

Answer 2

The magnetic field on the axis of a short bar magnet at distance $r$ is $B_{axis} = \frac{\mu_0}{4\pi} \frac{2M}{r^3}$. The magnetic field on the equatorial axis at distance $r'$ is $B_{equator} = \frac{\mu_0}{4\pi} \frac{M}{(r')^3}$. Given $B_{axis}(d_X) = B_{equator}(d_Y)$, we have $\frac{2M}{d_X^3} = \frac{M}{d_Y^3}$. This simplifies to $\frac{d_X^3}{d_Y^3} = \frac{1}{2}$, so $\frac{d_X}{d_Y} = (\frac{1}{2})^{1/3} = 2^{-1/3}$.