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20 April, 21:34

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?

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  1. 21 April, 01:07
    0
    (a) τ = 0.782Nm

    (b) x = 0.747Nm/rad

    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.
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