A circular coil of 185 turns has a radius of 1.60 cm. (a) Calculate the current that results in a magnetic dipole moment of magnitude 1.79 A·m2. (b) Find the maximum magnitude of the torque that the coil, carrying this current, can experience in a uniform 47.7 mT magnetic field.

(a) the current in the coil is 12.03 A

(b) the maximum magnitude of the torque is 0.0854 N. m

Explanation:

Given;

number of turns, N = 185

radius of the coil, r = 1.6 cm = 0.016 m

magnetic dipole moment, μ = 1.79 A·m²

Part (a) current in the coil

μ = NIA

Where;

I is the current in the coil

A is the of the coil = πr² = π (0.016) ² = 0.000804 m²

I = μ / (NA)

I = 1.79 / (185 x 0.000804)

I = 1.79 / 0.14874

I = 12.03 A

Part (b) the maximum magnitude of the torque

τ = μB

Where;

τ is the maximum magnitude of the torque

B is the magnetic field strength = 47.7 mT

τ = 1.79 x 0.0477 = 0.0854 N. m

Given Information:

Number of turns = N = 185 turns

Radius of circular coil = r = 1.60 cm = 0.0160 m

Magnetic field = B = 47.7 mT

Magnetic dipole moment = µ = 1.79 A. m

Required Information:

(a) Current = I = ?

(b) Maximum Torque = τ = ?

Answer:

(a) Current = 12.03 A

(b) Maximum Torque = 0.0853 N. m

Explanation:

(a) The magnetic dipole moment µ is given by

µ = NIAsin (θ)

I = µ/NAsin (θ)

Where µ is the magnetic dipole moment, N is the number of turns, I is the current flowing through the circular loop, A is the area of circular loop and is given by

A = πr²

A = π (0.0160) ²

A = 0.000804 m²

I = 1.79/185*0.000804*sin (90)

I = 12.03 A

(b) The toque τ is given by

τ = NIABsin (θ)

The maximum torque occurs at θ = 90°

τ = 185*12.03*0.00804*0.0477*sin (90°)

τ = 0.0853 N. m