The midpoint of two small magnetic dipoles d in end-on positions, are separated by a distance x,(.xd.). The force between them is proportional to x- n where n is:

Question

The midpoint of two small magnetic dipoles d in end-on positions, are separated by a distance x,(.x>>d.). The force between them is proportional to x- n where n is: (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

Magnetic field due to a magnetic dipole at the end-on position is

B = \frac{μ _{0}}{4 π} \frac{2 M}{r ^{3}}

.
Potential energy,

U = - μ \to \cdot B \to

.
i.e.,

U \propto \frac{1}{r ^{3}}

Force between the dipoles,

F = - \frac{d U}{d r}

.
Therefore, on differentiating the expression of potential energy, the force between them,

F \propto \frac{1}{r ^{4}}

or

F \propto r^{- 4}

.

Q. The midpoint of two small magnetic dipoles $d$ in end-on positions, are separated by a distance $x, (x >> d) .$ The force between them is proportional to $x^{- n}$ where $n$ is:

$1$

$2$

$3$

$4$

Q. The midpoint of two small magnetic dipoles d in end-on positions, are separated by a distance x,(x>>d). The force between them is proportional to x−n where n is:

1

2

3

4

Q. The midpoint of two small magnetic dipoles $d$ in end-on positions, are separated by a distance $x, (x >> d) .$ The force between them is proportional to $x^{- n}$ where $n$ is:

$1$

$2$

$3$

$4$