Question

Transcribed image text:

A wire loop with 50 turns is formed into a square with sides of length s. The loop is in the presence of a 3.5 T uniform magnetic field
B
that points in the negative y direction. The plane of the loop is tilted off the x− axis by θ=15. If i=2.70 A of current flows through the loop and the loop experiences a torque of magnitude 0.44 N⋅m, what are the lengths of the sides ss of the square loop, in centimeters? A wire loop with 50 turns is formed into a square with sides of length s. The loop is in the presence of a 3.5 T uniform magnetic field
B
that points in the negative y direction. The plane of the loop is tilted off the x axis by θ=15. If i=2.70 A of current flows through the loop and the loop experiences a torque of magnitude 0.44 N⋅m, what are the lengths of the sides ss of the square loop, in centimeters?

Answer 1

To find the lengths of the sides of the square loop, calculate the torque using the formula: Torque = N * B * I * A * sin(theta). Then use the formula A = Torque / (N * B * I * sin(theta)) to find the area. Finally, take the square root of the area to get the length of the sides of the square loop.

Step-by-step explanation:

To find the lengths of the sides of the square loop, we can first calculate the torque experienced by the loop.

The torque on a current-carrying loop in a magnetic field is given by the formula: Torque = N * B * I * A * sin(theta), where N is the number of turns, B is the magnetic field strength, I is the current, A is the area of the loop, and theta is the angle between the loop's normal and the magnetic field.

In this case, we are given the torque (0.44 N*m), the number of turns (50), the magnetic field strength (3.5 T), the current (2.70 A), and the angle (15 degrees). We can rearrange the formula and solve for the area of the loop: A = Torque / (N * B * I * sin(theta)).

Once we have the area, we can calculate the length of the sides of the square loop by taking the square root of the area: s = sqrt(A / N).