The Magnetic Dipole Moment

Concept: Magnetic dipole moment of a coil: Torque on current loop:
Step 1: Convert radius to metres.
Step 2: Area of circular coil.
Step 3: Magnetic dipole moment.
Step 4: Torque on coil. Final Answers:

[(i)] Magnetic dipole moment:
[(ii)] Counter torque required:

Concept: A current-carrying loop in a magnetic field experiences torque due to magnetic forces on its sides. Magnetic force on a current element:
Step 1: Consider rectangular loop.

Lengths: and
Area:
Area vector normal to plane of loop
Let magnetic field make angle with area vector.
Step 2: Forces on sides.

Two sides parallel to field → no force
Two sides perpendicular to field → equal and opposite forces
These forces form a couple producing torque.
Step 3: Magnitude of force. For side of length :
Step 4: Torque on loop. Torque = force × perpendicular distance between forces = Since :
Step 5: Magnetic dipole moment. Magnetic dipole moment of loop: So magnitude of torque:
Step 6: Vector form. The direction of torque is perpendicular to both and . Thus: Conclusion: A current loop behaves like a magnetic dipole and experiences torque tending to align its magnetic moment with the magnetic field.