A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45^{\circ}, and 40 times per minute where the dip is 30^{\circ}. 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 :

  • Option 1)

    2.2

  • Option 2)

    0.7

  • Option 3)

    1.8

  • Option 4)

    3.6

 

Answers (1)

Compass needle 1 \rightarrow 

Compass needle 2\rightarrow

I_{1}=\frac{1}{2\pi}\sqrt{\frac{rB_{1}\cos45^{\circ}}{I}}

I_{2}=\frac{1}{2\pi}\sqrt{\frac{rB_{2}\cos30^{\circ}}{I}}

\Rightarrow \frac{I_{1}}{I_{2}}=\sqrt{\frac{B_{1}\cos45^{\circ}}{B_{2}\cos30^{\circ}}}

\Rightarrow \frac{B_{1}}{B_{2}}=0.7


Option 1)

2.2

Option 2)

0.7

Option 3)

1.8

Option 4)

3.6

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