(a) The magnetic moment (μ) of a current loop is given by the product of the current (I) and the area (A) of the loop. The area of a circular loop is given by A = πr², where r is the radius of the loop. The radius can be found from the circumference (C) using the formula r = C / (2π).

Step 1: Calculate the radius of the loop.
r = C / (2π) = 3.80 m / (2π) = 0.604 m

Step 2: Calculate the area of the loop.
A = πr² = π * (0.604 m)² = 1.15 m²

Step 3: Calculate the magnetic moment.
μ = I * A = 30.0 mA * 1.15 m² = 34.5 mA·m²

(b) The torque (τ) exerted by a magnetic field on a current loop is given by τ = μBsinθ, where B is the magnetic field strength and θ is the angle between the magnetic field and the normal to the plane of the loop. In this case, the magnetic field is parallel to the plane of the loop, so θ = 90° and sinθ = 1.

Step 4: Calculate the torque.
τ = μBsinθ = 34.5 mA·m² * 0.510 T * sin(90°) = 17.6 mN·m

So, the magnetic moment of the loop is 34.5 mA·m² and the magnitude of the torque exerted by the magnetic field on the loop is 17.6 mN·m.

Question

(a) The magnetic moment (μ) of a current loop is given by the product of the current (I) and the area (A) of the loop. The area of a circular loop is given by A = πr², where r is the radius of the loop. The radius can be found from the circumference (C) using the formula r = C / (2π).

Step 1: Calculate the radius of the loop.
r = C / (2π) = 3.80 m / (2π) = 0.604 m

Step 2: Calculate the area of the loop.
A = πr² = π * (0.604 m)² = 1.15 m²

Step 3: Calculate the magnetic moment.
μ = I * A = 30.0 mA * 1.15 m² = 34.5 mA·m²

(b) The torque (τ) exerted by a magnetic field on a current loop is given by τ = μBsinθ, where B is the magnetic field strength and θ is the angle between the magnetic field and the normal to the plane of the loop. In this case, the magnetic field is parallel to the plane of the loop, so θ = 90° and sinθ = 1.

Step 4: Calculate the torque.
τ = μBsinθ = 34.5 mA·m² * 0.510 T * sin(90°) = 17.6 mN·m

So, the magnetic moment of the loop is 34.5 mA·m² and the magnitude of the torque exerted by the magnetic field on the loop is 17.6 mN·m.

Knowee AI · Accepted Answer

(a) The magnetic moment (μ) of a current loop is given by the product of the current (I) and the area (A) of the loop. The area of a circular loop is given by A = πr², where r is the radius of the loop. The radius can be found from the circumference (C) using the formula r = C / (2π).

Step 1: Calculate the radius of the loop.
r = C / (2π) = 3.80 m / (2π) = 0.604 m

Step 2: Calculate the area of the loop.
A = πr² = π * (0.604 m)² = 1.15 m²

Step 3: Calculate the magnetic moment.
μ = I * A = 30.0 mA * 1.15 m² = 34.5 mA·m²

(b) The torque (τ) exerted by a magnetic field on a current loop is given by τ = μBsinθ, where B is the magnetic field strength and θ is the angle between the magnetic field and the normal to the plane of the loop. In this case, the magnetic field is parallel to the plane of the loop, so θ = 90° and sinθ = 1.

Step 4: Calculate the torque.
τ = μBsinθ = 34.5 mA·m² * 0.510 T * sin(90°) = 17.6 mN·m

So, the magnetic moment of the loop is 34.5 mA·m² and the magnitude of the torque exerted by the magnetic field on the loop is 17.6 mN·m.

A current of 30.0 mA is maintained in a single circular loop of 3.80 m circumference. A magnetic field of 0.510 T is directed parallel to the plane of the loop.(a) Calculate the magnetic moment of the loop. mA · m2(b) What is the magnitude of the torque exerted by the magnetic field on the loop?

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