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
$U=-\overrightarrow{M}.\overrightarrow{B}$
$=\frac{\mu o}{4\pi }\frac{2M^2}{x^3}$
$F=-\frac{dU}{dx}=\frac{-3\mu o}{4\pi }\frac{2M^2}{x^4}$
therefore force between them $\propto {\text{x}}^{-4}$