Question

Two small bar magnets are placed in a line at a certain distance d part. If the length of each magnet is negligible compared to d, the force between them will be inversely proportional to:
A. ${{d}^{2}}$
B. $d$
C. ${{d}^{3}}$
D. ${{d}^{4}}$

Answer 1

Use the formula of force between two bar magnets.

Formula used: $F=\frac{{{\mu }_{0}}}{4\pi }\frac{6{{M}_{1}}{{M}_{2}}}{{{r}^{4}}}$
Here
F is force between two bar magnets
M1 and M2 are magnetic moments
r is the distance between bar magnets
$\mu_0$is permeability of free space

Complete step by step solution:
If the length of the bar magnets is negligible compared then $r=d$
Hence, the force acting between them will be proportion to $\frac{1}{d^4}$

The correct answer is option D.

Note: A bar magnet is a magnetic dipole. It is analogous to an electric dipole which is a system of two equal and opposite equal charges. Isolated magnetic charges or magnetic monopoles do not exist in nature. Even if a bar magnet is broken down to the atomic level, the north and south poles can never be separated.