Magnetism Question 26
Question: 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
Options:
A) Square of the distance
B) Cube of the distance
C) Distance
D) Fourth power of the distance
Show Answer
Answer:
Correct Answer: D
Solution:
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 }.\frac{2M _{1}}{r^{3}} $ By using $ F=-\frac{dU}{dr} $ , Force on magnet (2) is $ F _{2}=-\frac{dU _{2}}{dr}=-\frac{d}{dr}( \frac{{\mu _{0}}}{4\pi }.\frac{2M _{1}M _{2}}{r^{3}} )=-\frac{{\mu _{0}}}{4\pi }.6\frac{M _{1}M _{2}}{r^{4}} $ It can be proved $ | F _{1} |=| F _{2} |=F=\frac{{\mu _{0}}}{4\pi }.\frac{6M _{1}M _{2}}{r^{4}} $
$ \Rightarrow F\propto \frac{1}{r^{4}} $
BETA
