A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the varying magnetic field induced is observed to be 59 mT, what is the maximum value emf in the coil ?

4.19 V

Explanation:

Magnetic field flux and induced emf formula is:

Where

is the max emf (what we want)

N is the number of turns (N = 400)

A is the Area which is  ()

is the angular velocity ( , f is frequency, f = 90)

is the max magnetic field value (given as 59 mT)

Finding A, Area:

In meters squared, it would be:

A = 3.14 * 10^-4 meter squared

Calculating angular velocity:

Now, finding max EMF:

So, the max value emf in the coil is around 4.19 V

0.11 m/s and 0.28 m/s should be correct