question_answer

Force between two identical bar magnets whose Centres \[r\]meter apart is 4.8 N when their axis are in the same line. If the separation is increased to 2r meter, the force between them is reduced to:

A)  0.3 N                                    

B)  0.6 N

C)  2.4 N                                    

D)  1.2 N

Correct Answer: A

Solution :

Force between two magnets is given by \[F=\frac{{{\mu }_{\,0}}}{4\,\pi }\left( \frac{6\,{{M}_{1}}\,{{M}_{2}}}{{{r}^{4}}} \right)\] \[\Rightarrow \]                               \[F\propto \frac{1}{{{r}^{4}}}\] \[\therefore \]                  \[\frac{{{F}_{1}}}{{{F}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{4}}\]                                                 \[\frac{4.8}{{{F}_{2}}}={{\left( \frac{2r}{r} \right)}^{4}}=16\] \[\Rightarrow \]                               \[{{F}_{2}}=0.3\,N\]