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5.Magnetism and Matter
hard
Two magnets $A$ and $B $ are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point $P$ which gets deflected through an angle $\theta $ under the influence of magnets. The ratio of distance ${d_1}$ and ${d_2}$ will be
A
${(2\tan \theta )^{1/3}}$
B
${(2\tan \theta )^{ - 1/3}}$
C
${(2\cot \theta )^{1/3}}$
D
${(2\cot \theta )^{ - 1/3}}$
Solution
(c)In equilibrium ${B_1} = {B_2}\tan \theta $
$ \Rightarrow \frac{{{\mu _0}}}{{4\pi }}.\frac{{2M}}{{d_1^3}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{M}{{d_2^3}}\tan \theta $
$ \Rightarrow \frac{{{d_1}}}{{{d_2}}} = {\left( {2\cot \theta } \right)^{1/3}}$
Standard 12
Physics
