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) 2M^ 2 x^ 3 F = - (dU)/(dx) = (- 3 )/(4π) 2M^ 2 x^ 4 therefore force between them ∝ x^ - 4

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Magnetic Properties of Matter

NTA Abhyas 2020 · 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 to

x^{-

\text{n}

}

where n is :<br /> <br /> <img alt="" src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fnta_abhyas%252Fjee_main%252Fimages%252FEM0025910_AnsExp_1.jpg%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2FEM0025910_AnsExp_1.jpg?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2FEM0025910_AnsExp_1.jpg?alt=media" 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{{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}

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