A short bar magnet of magnetic moment m = 0.32 J T-1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its ( a ) stable, and ( b) unstable equilibrium? What is the potential energy of the magnet in each case?
A short bar magnet of magnetic moment m = 0.32 J T-1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its ( a ) stable, and ( b) unstable equilibrium? What is the potential energy of the magnet in each case?
Solution and Explanation
Moment of the bar magnet, M = 0.32 J T-1
External magnetic field, B = 0.15 T
( a ) The bar magnet is aligned along the magnetic field. This system is considered as being in stable equilibrium. Hence, the angle \(\theta\), between the bar magnet and the magnetic field is 0°.
Potential energy of the system = -MBcos \(\theta\)
= -0.32 × 0.15cos 0°
= -4.8 × 10-2 J
( b) The bar magnet is oriented 180° to the magnetic field. Hence, it is in unstable
equilibrium. \(\theta\) = 180°
Potential energy = − MB cos \(\theta\)
= -0.32 × 0.15cos180°
= 4.8 × 10-2 J
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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.