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
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?
(sin theta = 1)
Solve for r.
N = 1 in this case
The length of the wre is 2 pi r
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.