Question

The plane of a 5.0cm * 8.0cm rectangular loop of wire is parallelto a 0.19-T magnetic field. The loop carries a current of 6.2A. (a)What torque acts on the loop? (b) What is the magnetic moment ofthe loop? (c) What is the maximum torque that can be obtained withthe same total length of wire carrying the same current in thismagnetic field?

Answer 1

The torque acting on the loop is 0.004712 N*m. The magnetic moment of the loop is 0.0248 A*m². The maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field is 4.672 × 10-4 N*m.

Step-by-step explanation:

(a) To calculate the torque acting on the loop, we use the equation τ = μ × B, where μ is the magnetic dipole moment and B is the magnetic field strength. Firstly, we calculate the magnetic dipole moment: μ = NIA, where N is the number of turns, I is the current, and A is the area of the loop.

Given: N = 1 (since it's a single loop), I = 6.2 A, A = 5.0 cm * 8.0 cm = 40 cm² = 0.004 m². Substituting these values into the equation, we get: μ = (1)(6.2 A)(0.004 m²) = 0.0248 A*m².

Now, plugging this value and the given magnetic field strength B = 0.19 T into the torque formula, we have: τ = (0.0248 A*m²)(0.19 T) = 0.004712 N*m.

Therefore, the torque acting on the loop is 0.004712 N*m.

(b) The magnetic moment of the loop is the same as the magnetic dipole moment, which is 0.0248 A*m².

(c) To find the maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field, we need to consider the maximum torque formula τ = NIA(Bsinθ), where θ is the angle between the magnetic field and the normal to the plane of the loop.

The maximum torque occurs when sinθ = 1, so the maximum torque is τ = NIA(B)(1) = NIA(B).

The total length of wire in the loop is the perimeter of the rectangle. Given that the sides of the rectangle are 5.0 cm and 8.0 cm, the perimeter is (2 * 5.0 cm) + (2 * 8.0 cm) = 26.0 cm = 0.26 m.

Substituting the values of N = 1, I = 6.2 A, A = 0.004 m², and B = 0.19 T into the maximum torque formula, we have: τ = (1)(6.2 A)(0.004 m²)(0.19 T) = 4.672 × 10-4 N*m.

Therefore, the maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field is 4.672 × 10-4 N*m.

Answer 2

The torque acting on a rectangular loop of wire in a magnetic field can be calculated using the equation: Torque = magnetic moment * magnetic field. To calculate the torque, you need to find the magnetic moment of the loop, which is given by the equation: Magnetic moment = current * area of the loop. Substituting the given values will allow you to calculate the torque.

Step-by-step explanation:

The torque acting on a rectangular loop of wire in a magnetic field can be calculated using the equation:

Torque = magnetic moment * magnetic field

To calculate the torque, we first need to find the magnetic moment of the loop, which is given by the equation:

Magnetic moment = current * area of the loop

Given that the loop has dimensions of 5.0 cm * 8.0 cm and the current is 6.2 A, we can calculate the magnetic moment:

Magnetic moment = 6.2 A * (5.0 cm * 8.0 cm)

Then, we can calculate the torque:

Torque = magnetic moment * magnetic field

Substituting the values, we get:

Torque = (6.2 A * (5.0 cm * 8.0 cm)) * 0.19 T

Solving this equation will give you the value of the torque acting on the loop.

To calculate the magnetic moment, maximum torque, and potential energy for a loop with the same current and total wire length in the same magnetic field, you would need to know the dimensions of the loop (length and width).