Question

The mid points of two small magnetic dipoles of length $\text{d}$ in end-on positions, are separated by a distance $\text{x}$ $\left(\text{x} > > \text{d}\right)$ . The magnitude of force between them is proportional to $\text{x}^{- \text{n}}$ where n is :

• A. $3$
• B. $4$
• C. $2$
• D. $1$

Answer 1

Answer: (B)

$\text{B} = \frac{\mu _{\text{o}}}{4 \pi } \frac{2 \text{M}}{\text{x}^{3}}$ for end-on position
$U=-\overset{ \rightarrow }{M}.\overset{ \rightarrow }{B}$
$=\frac{\mu o}{4 \pi }\frac{2 M^{2}}{x^{3}}$
$F=-\frac{d U}{d x}=\frac{- 3 \mu o}{4 \pi }\frac{2 M^{2}}{x^{4}}$
therefore force between them $ \propto \text{x}^{- 4}$