Question:
A thin circular disk of radius $R$ is uniformly charged with density $\sigma$ > 0 per unit area. The disk rotates about its axis with a uniform angular speed $\omega$. The magnetic moment of the disk is :
A thin circular disk of radius $R$ is uniformly charged with density $\sigma$ > 0 per unit area. The disk rotates about its axis with a uniform angular speed $\omega$. The magnetic moment of the disk is :
Updated On: Jul 31, 2023
- $\pi R^{4}\sigma\omega$
- $\frac{\pi R^{4}}{2}\sigma\omega$
- $\frac{\pi R^{4}}{4}\sigma\omega$
- $2\pi R^{4}\sigma\omega$
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The Correct Option is C
Solution and Explanation
$\frac{q}{2M} = \frac{Magnetic \,dipole \,moment}{Angular \,momentum}$
$\therefore\quad$ Magnetic dipole moment (M)
$M = \frac{q}{2M}. \left(\frac{MR^{2}}{2}\right)\omega$
$= \frac{1}{4}\sigma.\pi R^{4}\omega$
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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.