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
Top Questions on Magnetism and matter
- A coil of 60 turns and area \( 1.5 \times 10^{-3} \, \text{m}^2 \) carrying a current of 2 A lies in a vertical plane. It experiences a torque of 0.12 Nm when placed in a uniform horizontal magnetic field. The torque acting on the coil changes to 0.05 Nm after the coil is rotated about its diameter by 90°. Find the magnitude of the magnetic field.
- CBSE CLASS XII - 2025
- Physics
- Magnetism and matter
A current-carrying coil is placed in an external uniform magnetic field. The coil is free to turn in the magnetic field. What is the net force acting on the coil? Obtain the orientation of the coil in stable equilibrium. Show that in this orientation the flux of the total field (field produced by the loop + external field) through the coil is maximum.
- CBSE CLASS XII - 2025
- Physics
- Magnetism and matter
- Obtain the relation for magnetic dipole moment \( \mathbf{M} \) of a current-carrying coil. Give the direction of \( \mathbf{M} \).
- CBSE CLASS XII - 2025
- Physics
- Magnetism and matter
- A current-carrying loop can be considered as a magnetic dipole placed along its axis. Explain.
- CBSE CLASS XII - 2025
- Physics
- Magnetism and matter
- A diamagnetic substance is brought, one by one, near the north pole and the south pole of a bar magnet. It is:
- CBSE CLASS XII - 2025
- Physics
- Magnetism and matter
Questions Asked in CBSE CLASS XII exam
- \[ \int \frac{\tan^2 \sqrt{x}}{\sqrt{x}} \, dx \text{ is equal to:} \]
If \(\begin{vmatrix} 2x & 3 \\ x & -8 \\ \end{vmatrix} = 0\), then the value of \(x\) is:
- Find the maximum slope of the curve \( y = x^3 + 3x^2 + 9x - 30 \).
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Application of derivatives
- Differentiate $2\cos^2 x$ w.r.t. $\cos^2 x$.
- CBSE CLASS XII - 2025
- Derivatives
- Arushi, Vivaan and Mitali were partners in a firm. On 31st March 2024, the firm was dissolved. On that date, the firm had debtors of \( ₹ 60,000 \) and provision for doubtful debts of \( ₹ 3,000 \) were existing in the books. Debtors of \( ₹ 8,000 \) proved bad and full amount was realised from the remaining debtors. The amount realised from debtors was:
- CBSE CLASS XII - 2025
- Dissolution of Partnership Firms
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.