Final answer:
The peak emf generated by rotating the coil is 20.0 V. Faraday's law of electromagnetic induction can be used to calculate the average emf, which is equal to the peak emf in this case. By calculating the change in magnetic flux and dividing it by the time interval of rotation, we can determine the peak emf.
Step-by-step explanation:
To determine the peak emf generated by rotating the coil, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf is equal to the rate of change of magnetic flux through the coil. In this case, the coil is rotated from perpendicular to parallel to the magnetic field in 10.0 ms, which corresponds to a change in angle of 90 degrees.
The magnetic flux through the coil is given by the product of the magnetic field strength, the area of the coil, and the cosine of the angle between the field and the normal to the coil.
The diameter of the coil is 20.0 cm, so the radius is 10.0 cm or 0.1 m. The area of the coil is given by π times the square of the radius. The angle between the field and the normal to the coil is 90 degrees when the coil is perpendicular to the magnetic field, and 0 degrees when the coil is parallel to the field.
By substituting the given values into the equation for magnetic flux, and multiplying by the number of turns in the coil, we can calculate the change in magnetic flux. Finally, by dividing the change in magnetic flux by the time interval of rotation, we can calculate the average emf generated. The peak emf will be equal to the average emf since the rotation is linear and the emf does not vary during the rotation.
Using the given values and substituting into the equations, we find that the peak emf generated by rotating the coil is 20.0 V (option c).