Question

Consider a 50-turn circular loop with a radius of 1.75 cm in a 0.25-T magnetic field. This coil is going to be used in a galvanometer that reads 65 for a full-scale deflection. Such devices use spiral springs which obey an angular form of Hooke's law, where the restoring torque is Here x is the torque constant and ? is the angular displacement, in radians, of the spiral spring from equilibrium, where the magnetic field and the normal to the loop are parallel ? 50%

Part (a) Calculate the maximum torque, in newton meters, on the loop when the full-scale current flows in it
Part (b) What is the torque constant of the spring, in newton meters per radian, that must be used in this device?

Answer 1

(a) τ = 0.782Nm

(b) x = 0.747Nm/rad

Step-by-step explanation:

Given that

N = 50, r = 1.75cm = 1.75×10-²m, B = 0.25T, I = 65A.

The torque on a coil of N turns of wire is given by

τ = NIAB

From the problem statement, this torque can also be represented by an angular form of hooke's law.

τ = xθ

Where N = number of turns, I = current in amps (A), A = area in m², B = magnetic field strength in T, x = torque constant in Nm/rad and θ = angular displacement.

Area A = πr² = π×(1.75×10-²)² = 9.62×10-⁴m²

(a) τ = NIAB = 50×65×9.62×10-⁴×0.25

τ = 0.782Nm

(b) x = τ/θ

θ = 60° = 60×2π/360 = π/3 rad

x = 0.782/(π/3)

x = 0.747Nm/rad.