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Q.

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

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a

3 : 1

b

3 : 2

c

$\sqrt{3} : 1$

d

$2 \sqrt{3} : 1$

answer is D.

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Detailed Solution

$\begin{array}{rcl} B & = & B_{H} tanθ; \\ \frac{μ_{0}}{4 π} \frac{2 M}{d^{3}} & = & B_{H} tanθ; \\ M α tanθ \\ \frac{M_{1}}{M_{2}} = \frac{{tanθ}_{1}}{{tanθ}_{2}} \Rightarrow \frac{m_{1} L_{1}}{m_{2} L_{2}} = \frac{{tanθ}_{1}}{{tanθ}_{2}} \end{array}$

$\frac{m_{1}}{m_{2}} = \frac{2}{1} x \frac{\tan 45^{o}}{\tan 30^{o}} = \frac{2 \sqrt{3}}{1}$

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