A circular loop is placed in an external magnetic field. How is the torque 'τ' related to radius 'r' of the loop?

The correct answer is option 2) i.e. 

CONCEPT:

• Torque on a current loop: A current-carrying loop placed in a magnetic field will experience multiple magnetic forces on it due to the change in direction of current along the loop. Any two such equal and opposite force forms a couple and causes torque in the loop.
  • The torque experienced by a current-carrying loop placed in a magnetic field is the vector product of the magnetic moment and the magnetic field.

It is given by:

Torque, τ = m × B

Where m is the magnetic moment and B is the magnetic field intensity.

• The magnetic moment is the product of the current flowing in the loop and the area of the loop.

It is given by:

Magnetic moment, m = IA

Where I is the current and A is the area.

EXPLANATION:

The torque acting on the loop, τ = m × B = IAB

• Since the loop is circular, area A = πr² (where r is the radius of the circular loop)

⇒ τ = IB(πr²)

⇒ τ ∝ r2