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 :

Updated On: Jul 8, 2024

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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 $

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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.