Exam

JEE Main

Subject

Physics

Chapter

Magnetic Properties of Matter

JEE Main · Physics · Magnetic Properties of Matter

The mid points of two small magnetic dipoles of length d in end-on...

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 tox^{- \text{n}} where n is :

Step-by-step solution

$\text{B} = \dfrac{{μ}_{o}}{4 \pi} \dfrac{2 \text{M}}{x^{3}}$ for end-on position

$U = - \overset{→}{M} . \overset{→}{B}$

$= \dfrac{\muo}{4\pi} \dfrac{2M^{2}}{x^{3}}$

$F = - \dfrac{dU}{dx} = \dfrac{- 3\muo}{4\pi} \dfrac{2M^{2}}{x^{4}}$

therefore force between them $∝ x^{- 4}$