The effects due to the interaction of a current-carrying loop with a magnetic field have many applications, some as common as the electric motor. This problem illustrates the basic principles of this interaction.

Consider a current I that flows in a plane rectangular current loop with height a = 4.00cm and horizontal sides b = 2.00cm. The loop is placed into a uniform magnetic field B? in such a way that the sides of length a are perpendicular to B? , and there is an angle ? between the sides of length b and B?.

For parts A and B, the loop is initially positioned at ?=30? .

A) Assume that the current flowing into the loop is 0.500A . If the magnitude of the magnetic field is 0.300T , what is ?, the net torque about the vertical axis of the current loop due to the interaction of the current with the magnetic field?

B) What happens to the loop when it reaches the position for which ?=90?, that is, when its horizontal sides of length b are perpendicular to B?.
- The direction of rotation changes because the net torque acting on the loop causes the loop to rotate in a clockwise direction.
- The net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction.
- The net torque acting on the loop is zero; therefore it stops rotating.
- The net force acting on the loop is zero, so the loop must be in equilibrium.

The torque τ acting on a current-carrying loop of area A due to the interaction of the current I flowing through the loop with a magnetic field of magnitude B is given by

τ = I*B*A*Sin∅

where ∅ is the angle between the normal to the loop and the direction of the magnetic field.

The area A of a rectangular loop of wire with height 4.00 cm and horizontal sides 2.00 cm can be obtained as follows

Aloop = a*b ⇒ Aloop = 0.04 m*0.02 m = 8*10⁻⁴m²

Recalling that θ is the angle between the sides of length b and B and if we consider the normal to the loop, the angle ∅ between the normal and the magnetic field is given by

∅ = 90°-θ ⇒ ∅ = 90°-30° = 60°

Then, the torque will be

τ = (0.5 A)*(0.3 T)*(8*10⁻⁴m²)*Sin60° = 1.039*10⁻⁴N-m

b) We have to get the net torque τ about the vertical axis of the current loop due to the interaction of the current with the magnetic field.

The angle ∅ between the normal to the loop and the magnetic field when the horizontal sides of the loop of length b are perpendicular to B is

∅ = 0°

Then

τ = (0.5 A)*(0.3 T)*(8*10⁻⁴m²)*Sin 0° = 0 N-m

We can say that the net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction.

ConcepcionPetillo ConcepcionPetillo · Answer 2 · 2025-03-27T15:12:06-04:00

(a) The net torque is 1.039 × 10⁻⁴ Nm

(b) The net torque is zero, but it continues to rotate in a counterclockwise direction.

Magnetic field and torque:

Given information:

current in the loop I = 0.5 A

magnetic field B = 0.3 T

height of the loop a = 4 cm = 0.04 m

horizontal sides b = 2 cm = 0.02 m

The angle between the plane of the loop and magnetic field θ = 30°

The torque τ acting on a current-carrying loop of area A due to the

τ = IBAsin∅

where ∅ is the angle between the area vector and the direction of the magnetic field.

Area of the loop:

A = ab = 0.04 × 0.02

A = 8 × 10⁻⁴ m²

The angle ∅ between the area vector and the magnetic field is given by

∅ = 90°-θ = 60°

Then, the torque will be:

τ = 0.5 × 0.3 × 8 × 10⁻⁴ × sin60°

τ = 1.039 × 10⁻⁴ Nm

(b) The angle ∅ between the normal to the loop and the magnetic field when the horizontal sides of the loop of length b are perpendicular to B is

∅ = 0°

Thus

τ = IBAsin∅

τ = IBAsin0°

τ = 0

It implies that the net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction.

Learn more about torque:

https://brainly.com/question/13795320?referrer=searchResults

https://brainly.com/question/3388202?referrer=searchResults