A coil with 163 turns and a radius of 1.5 cm carries a current of 1.70 A. It is placed in a uniform 3.0 T magnetic field. Find the torque exerted on the coil by this field if the normal to the plane of the coil is oriented perpendicular to the field. Express your answer in Newton-meters to two significant figures.

Question

22-04-2025
Physics

High School

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A coil with 163 turns and a radius of 1.5 cm carries a current of 1.70 A. It is placed in a uniform 3.0 T magnetic field. Find the torque exerted on the coil by this field if the normal to the plane of the coil is oriented perpendicular to the field. Express your answer in Newton-meters to two significant figures.

Answer :

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professorenglish94 professorenglish94 · Answer 1 · 2024-09-24T02:09:14-04:00

The torque exerted on the coil is approximately 7.8 Nm.

First, we calculate the torque (τ) using the formula: τ = NIBsin(θ), where N is the number of turns in the coil, I is the current flowing through the coil, B is the magnetic field strength, and θ is the angle between the magnetic field and the normal to the coil's plane.

Given:

N = 163 turns,

I = 1.70 A,

B = 3.0 T,

θ = 90° (since the normal plane of the coil is perpendicular to the field).

Substituting the given values into the formula:

τ = (163)(1.70)(3.0)sin(90°).

Since sin(90°) = 1, the calculation simplifies to:

τ = (163)(1.70)(3.0)(1).

Now, performing the multiplication:

τ = 782.1 Nm.

Therefore, the torque exerted on the coil is approximately 782.1 Nm. However, we need to express the answer to two significant figures.

Rounding to two significant figures:

τ ≈ 7.8 Nm.

This represents the torque exerted by the magnetic field on the coil when its normal plane is oriented perpendicular to the field. The torque value indicates the rotational force experienced by the coil.