Question:
If the work done in turning a magnet of magnetic moment $M$ by an angle of 90$^{\circ}$ from the magnetic meridian is $n$ times the corresponding work done to turn it through an angle of 60$^{\circ}$, then the value of $n$ is
If the work done in turning a magnet of magnetic moment $M$ by an angle of 90$^{\circ}$ from the magnetic meridian is $n$ times the corresponding work done to turn it through an angle of 60$^{\circ}$, then the value of $n$ is
Updated On: Apr 15, 2024
- 1
- 2
- $\frac{1}{2}$
- $\frac{1}{4}$
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The Correct Option is B
Solution and Explanation
We have, $W=-M B\left(\cos \theta_{2}-\cos \theta_{1}\right)$
So, $W_{1}=-M B\left(\cos 90^{\circ}-\cos 0^{\circ}\right)=M B$
and $W_{2}=-M B\left(\cos 60^{\circ}-\cos 0^{\circ}\right)=\frac{1}{2} M B$
As $W_{1}=n W_{2}$
$\therefore n=\frac{W_{1}}{W_{2}}=\frac{M B}{\frac{1}{2} M B}=2$
So, $W_{1}=-M B\left(\cos 90^{\circ}-\cos 0^{\circ}\right)=M B$
and $W_{2}=-M B\left(\cos 60^{\circ}-\cos 0^{\circ}\right)=\frac{1}{2} M B$
As $W_{1}=n W_{2}$
$\therefore n=\frac{W_{1}}{W_{2}}=\frac{M B}{\frac{1}{2} M B}=2$
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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.