The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance x…

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

1. $3$
2. $4$
3. $2$
4. $1$

Solution

 

$\text{B}=\frac{{\mu }_{\text{o}}}{4\pi }\frac{2\text{M}}{{\text{x}}^3}$ 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 $\propto {\text{x}}^{-4}$

Asked in: JEE Main 2014 (09 Apr Online)

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