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

Correct answer: B. 4 B = μ _ o 4 π 2 M x ^ 3 for end-on position U = - → M . → B = ( )/(4π) 2 M ^ 2 x ^ 3 F = - (dU)/(dx) = (- 3 )/(4π) 2 M ^ 2 x ^ 4 therefore force between them ∝ x ^ - 4

JEE Main 20149 AprilOnline

Exam: JEE Main
Year: 2014
Date: 9 April
Mode: Online
Subject: Physics
Chapter: Magnetic Properties of Matter

JEE Main 2014 · 9 April · Online · 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

d

in end-on positions, are separated by a distance

x\left(x ≫ d\right). The magnitude of force between them is proportional to

{x}^{- n}

where

is :<br /><br /><img alt="" src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/EM0025910_AnsExp_1.jpg" style="width: 286px; height: 64px;" />

Options

A $3$
B $4$
C $2$
D $1$

Correct answer

B. $4$

Step-by-step solution

\text{B} = \dfrac{{\mu}_{\text{o}}}{4 \pi} \dfrac{2 \text{M}}{{\text{x}}^{3}}

for end-on position

U = - \overset{\to}{M} . \overset{\to}{B}

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

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

therefore force between them

∝ {\text{x}}^{- 4}

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