Magnetism Question 36
Question: 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
Options:
A) $ {{(2\tan \theta )}^{1/3}} $
B) $ {{(2\tan \theta )}^{-1/3}} $
C) $ {{(2\cot \theta )}^{1/3}} $
D) $ {{(2\cot \theta )}^{-1/3}} $
Show Answer
Answer:
Correct Answer: C
Solution:
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}}={{( 2\cot \theta )}^{1/3}} $
BETA
