MCQ
Two short magnets placed along the same axis with their like poles facing each other repel each other with a force which varies inversely as
- ASquare of the distance
- BCube of the distance
- CDistance
- ✓Fourth power of the distance
✓
Answer
Correct option: D.
Fourth power of the distance
Both the magnets are placed in the field of one another, hence potential energy of dipole (2) is
$U_2=-M_2 B_1 \cos 0=-M_2 B_1=M_2 \times \frac{\mu_0}{4 \pi} \cdot \frac{2 M_1}{r^3}$
By using $F=-\frac{d U}{d r}$, Force on magnet (2) is
$F_2=-\frac{d U_2}{d r}=-\frac{d}{d r}\left(\frac{\mu_0}{4 \pi} \cdot \frac{2 M_1 M_2}{r^3}\right)=-\frac{\mu_0}{4 \pi} \cdot 6 \frac{M_1 M_2}{r^4}$
It can be proved $\left|F_1\right|=\left|F_2\right|=F=\frac{\mu_0}{4 \pi} \cdot \frac{6 M_1 M_2}{r^4}$
$\Rightarrow F \propto \frac{1}{r^4}$
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