A flat, 193 193 ‑turn, current‑carrying loop is immersed in a uniform magnetic field. The area of the loop is 4.55 cm 2 4.55 cm2 and the angle between its magnetic dipole moment and the field is 59.1 ∘. 59.1∘. Find the strength B B of the magnetic field that causes a torque of 1.47 * 10 - 5 N ⋅ m 1.47*10-5 N⋅m to act on the loop when a current of 2.13 mA 2.13 mA flows in it.

0.0916 T

Explanation:

Parameters given:

Number of turns, N = 193

Area of loop, A = 4.55cm² = 0.000455 m²

Angle, θ = 59.1°

Torque, τ = 1.47 * 10^ (-5) Nm

Current, I = 2.13 mA = 0.00213 A

Using the formula for torque, we can find the magnetic field, B:

τ = N * I * A * B * sinθ

=> B = τ / (N * I * A * sinθ)

B = (1.47 * 10^ (-5)) / (193 * 2.13 * 10^ (-3) * 0.000455 * sin59. 1)

B = 0.0916 T

Given Information:

Torque = τ = 1.47*10⁻⁵ N. m

Current = I = 2.13 mA = 0.00213 A

Number of turns = N = 193

Angle = θ = 59.1°

Area = A = 4.55 cm² = 0.000455 m²

Required Information:

Magnetic field = B = ?

Answer:

Magnetic field = 9.159*10⁻² T

Explanation:

The toque τ is given by

τ = NIABsin (θ)

B = τ/NIAsin (θ)

Where N is the number of turns, I is the current flowing through the loop, A is the area of flat loop and θ is angle between magnetic dipole moment and magnetic field B,

B = 1.47*10⁻⁵ / (193*0.00213*0.000455*sin (59.1))

B = 9.159*10⁻² T

Therefore, the strength of the magnetic field is 9.159*10⁻² T.