A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is

Concept:

Magnetic dipole consists of two poles of magnet i.e., north and south pole separated by very small distance. Current loop acts as magnetic dipole.

The strength of the magnetic dipole is known as the magnetic dipole moment . It is given by M = NIA, where N is number of turns, I is current flowing through the loop, A is the area of loop.

The magnetic dipole moment is a vector quantity and its direction is given by the right-hand thumb rule.

Work done in rotating the coil through θ1 to θ2

W = MB (cosθ1 - cosθ2)

Where M is magnetic dipole moment, B is strength of magnetic field.

Calculation:

Number of turns, N = 250

Length = 2.1 cm

Width = 1.25 cm

Current, I = 85 μA 

Magnetic field of strength, B = 0.85 T

Work done for rotating the coil by 180° against the torque is, W = MB (cosθ₁ - cosθ₂)

When it is rotated by angle 180° then

W = 2MB

W = 2 (NIA)B

= 2 × 250 × 85 × 10^-6[1.25 × 2.1 × 10^-4] × 85 × 10^-2

= 9.1 μJ