A rectangular current carrying loop is placed in the magnetic field. If the magnetic field intensity is increased then the magnetic moment of the loop will:

CONCEPT:

Torque on a rectangular current loop in a uniform magnetic field:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
  • The net force on the loop will be zero.
• The torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB.sinθ

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The magnetic moment m for the loop is given as,

⇒ m = NIA

So,

\(⇒ τ = mB\,sinθ = \vec{m}\times\vec{B}\)

EXPLANATION:

• We know that the magnetic moment m for the current-carrying loop is given as,

⇒ m = NIA     -----(1)

Where N = number of turns in the coil, I = current in the loop, and A = area enclosed by the loop

• By equation 1 it is clear that the magnetic moment of the current-carrying loop does not depend on the magnetic field intensity.
• Therefore when the magnetic field intensity is increased, the magnetic moment of the loop will not change. Hence, option 3 is correct.