Question

# A magnetic compass needle oscillates $$30$$ times per minute at a place where the dip is $$45^o$$, and $$40$$ times per minute where the dip is $$30^o$$. If $$B_1$$ and $$B_2$$ are respectively the total magnetic field due to the earth at the two places, then the ratio $$B_1/B_2$$ is best given by :

A
2.2
B
1.8
C
0.7
D
3.6

Solution

## The correct option is C $$0.7$$$$f_1 = \dfrac{1}{2\pi} \sqrt{\dfrac{\mu B_1 \cos 45^o}{I}}$$$$f_2 = \dfrac{1}{2\pi} \sqrt{\dfrac{\mu B_2\cos 30^o}{I}}$$$$\dfrac{f_1}{f_2} = \sqrt{\dfrac{B_1 \cos 45^o}{B_2 \cos 30^o}}$$$$\therefore \dfrac{B_1}{B_2} = 0.7$$Physics

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