Magnetism Question 127

Question: When two magnetic moments are compared using equal distance method the deflections produced are 45o and 30o. If the length of magnets are in the ratio 1 : 2, the ratio of their pole strengths is

[JIPMER 2002]

Options:

A) 3 : 1

B) 3 : 2

C) $ \sqrt{3}:1 $

D) $ 2\sqrt{3}:1 $

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Answer:

Correct Answer: D

Solution:

$ \frac{M _{1}}{M _{2}}=\frac{\tan {\theta _{1}}}{\tan {\theta _{2}}}\Rightarrow \frac{m _{1}L _{1}}{m _{2}L _{2}}=\frac{\tan {\theta _{1}}}{\tan {\theta _{2}}} $
$ \Rightarrow \frac{m _{1}}{m _{2}}=\frac{2}{1}\times \frac{\tan 45{}^\circ }{\tan 30{}^\circ }=\frac{2\sqrt{3}}{1} $