The coil in a generator has 200 windings and a cross-sectional area of 0.0100 m^2.

If the coil turns at a constant rotational speed and the magnetic field in the generator is that of Earth (B = 0.500 × 10^-4 T), how many 360 rotations must the coil complete each second to generate a maximum induced emf of 2.00V ?

To find out how many 360 rotations the coil must complete each second, we need to use the formula for the induced electromotive force (emf) in a generator:

emf = N * B * A * ω

where:
- emf is the induced electromotive force (in volts)
- N is the number of windings in the coil
- B is the magnetic field strength (in teslas)
- A is the area of the coil (in square meters)
- ω is the angular velocity (in radians per second)

We can rearrange this formula to solve for ω:

ω = emf / (N * B * A)

Substituting the given values:
emf = 2.00 V
N = 200 windings
B = 0.500 × 10^-4 T
A = 0.0100 m^2

ω = 2.00 / (200 * 0.500 × 10^-4 * 0.0100)

Let's calculate this:

First, multiply 0.500 × 10^-4 by 0.0100:

0.500 × 10^-4 * 0.0100 = 5.00 × 10^-6

Now, calculate the denominator:

200 * 5.00 × 10^-6 = 1.00 × 10^-3

Finally, divide the emf by the denominator:

ω = 2.00 / (1.00 × 10^-3)

ω = 2.00 × 10^3 radians per second

This means the coil must complete 2000 rotations (or 360° rotations) each second to generate a maximum induced emf of 2.00 V.