Question:
A magnetic dipole of magnetic moment $6 \times 10^{-2} \, {Am^{2}}$ and moment of inertia $12 \times 10^{-6} \, {kg\, m^{2}}$ performs oscillations in a magnetic field of $2 \times 10^{-2} $ T. The time taken by the dipole to complete $20$ oscillations is $( \pi \simeq 3)$
A magnetic dipole of magnetic moment $6 \times 10^{-2} \, {Am^{2}}$ and moment of inertia $12 \times 10^{-6} \, {kg\, m^{2}}$ performs oscillations in a magnetic field of $2 \times 10^{-2} $ T. The time taken by the dipole to complete $20$ oscillations is $( \pi \simeq 3)$
Updated On: Apr 15, 2024
- 36 s
- 6 s
- 12 s
- 18 s
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The Correct Option is C
Solution and Explanation
Given,
Magnetic moment $(M)=6 \times 10^{-2} \,A - m ^{2}$
Moment of inertia $(I)=12 \times 10^{-6} kg - m ^{2}$
Magnetic field $(B)=2 \times 10^{-2} T$
We know that. Time $(t)=2 \pi \sqrt{\frac{I}{M B}}$
$=2 \pi \sqrt{\frac{12 \times 10^{-6}}{6 . \times 10^{-2} \times 2 \times 10^{-2}}} $
$=2 \pi \sqrt{\frac{12 \times 10^{-2}}{12}} $
$=2 \pi \times 10^{-1}$
For 20 oscillation,
Time $(t)=20 \times 2 \pi \times 10^{-1}$
$=12 s$
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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.