The maximum torque experienced by a coil in a 0.90 T magnetic field is 8.4 10-4 N·m. The coil is circular and consists of only one turn. The current in the coil is 3.9 A. What is the length of the wire from which the coil is made?

Please tell me if I am going in the right direction.

Torque = NIAB sin theta
8.4x10^-4 = 1 x 3.9 x (pi r^2) x 0.9 x sin theta

How do I find the value of sin theta to plug into the formula?

They give you the maximum torque, and that corresponds to theta = 90 degrees

(sin theta = 1)
Solve for r.
N = 1 in this case

The length of the wre is 2 pi r

To find the value of sin theta, we need to consider the geometry of the coil. You mentioned that the coil is circular and consists of only one turn. In this case, the coil forms a single loop, and theta represents the angle between the normal to the coil and the magnetic field.

Since the coil is circular and has one turn, we can consider it as a flat disk. The normal to the coil is perpendicular to the plane of the disk. When the magnetic field is parallel to the plane of the disk, the angle between the normal and the magnetic field is 90 degrees. This means sin theta in this case is equal to 1.

Therefore, in the given problem, sin theta = 1.

Substituting this value into the formula:

Torque = NIAB sin theta
8.4x10^-4 = 1 x 3.9 x (π r^2) x 0.9 x 1

Now you have the equation with only one unknown, which is the radius (r) of the coil. You can solve this equation for the radius and then proceed to find the length of the wire from which the coil is made.