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.

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 =  ?

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.