Question:
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 :
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 :
Updated On: July 22, 2025
- 2.2
- 1.8
- 0.7
- 3.6
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The Correct Option is C
Solution and Explanation
$f_{1} = \frac{1}{2\pi} \sqrt{\frac{\mu B_{1} \cos45^{\circ}}{I}} f_{2} = \frac{1}{2\pi } \sqrt{ \frac{\mu B_{2} \cos30^{\circ}}{I }} $
$ \frac{f_{1}}{f_{2}} = \sqrt{\frac{B_{1}\cos 45^{\circ}}{B_{2} \cos30^{\circ}}} \therefore \frac{B_{1}}{B_{2}} = 0.7 $
$ \frac{f_{1}}{f_{2}} = \sqrt{\frac{B_{1}\cos 45^{\circ}}{B_{2} \cos30^{\circ}}} \therefore \frac{B_{1}}{B_{2}} = 0.7 $
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.