Magnetism And Matter

The torque on a coil in a magnetic field is given by: Given that , we solve for : Using trigonometric identities, Thus, the correct answer is .

The magnetic field at the center of a regular polygon formed by a current-carrying wire is given by the formula: For a regular hexagon, the number of sides is 6, and the radius is the distance from the center to a side. Given that the side length is 2 cm, we can use the geometry of the hexagon to find the radius. The magnetic field is calculated as: Thus, the magnetic field at the center is .

Step 1: Define Magnetic Dipole Moment For a rotating charged ring, the magnetic dipole moment is given by: where is the current and is the area.
Step 2: Compute Current Total charge on the ring: The time period of rotation: Thus, current:
Step 3: Compute Magnetic Dipole Moment The area of the ring is: