Question:
A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is
A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is
Updated On: Apr 29, 2024
- $ 60^{\circ} $
- $ 45^{\circ} $
- $ 30^{\circ} $
- $ 75^{\circ} $
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The Correct Option is A
Solution and Explanation
$ \tau = MB \sin\,\theta $
where $ \theta=90^{\circ} $
$ \therefore \tau-MB $
Given $ \tau_2=\frac{1}{2}\tau_1 $
$ \therefore MB \sin\theta=\frac{1}{2}MB $
$ \therefore \sin \theta=\frac{1}{2} $
$ \Rightarrow \theta=30^{\circ} $
Angle of rotation is = $ 90^\circ-30^{\circ}=60^{\circ} $
where $ \theta=90^{\circ} $
$ \therefore \tau-MB $
Given $ \tau_2=\frac{1}{2}\tau_1 $
$ \therefore MB \sin\theta=\frac{1}{2}MB $
$ \therefore \sin \theta=\frac{1}{2} $
$ \Rightarrow \theta=30^{\circ} $
Angle of rotation is = $ 90^\circ-30^{\circ}=60^{\circ} $
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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.
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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.