A coil 4.15 cm radius, containing 560 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 3.40×10−5 T/s4 )t4. The coil is connected to a 530-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. (a) Find the magnitude of the induced emf in the coil as a function of time.
(b) What is the current in the resistor at time t = 5.00 s?

(a)

(b) I = 1.65*10^-4 A

Explanation:

(a) To find the induced emf in the coil you use the following formula:

          (1)

N: turns = 560

ФB: magnetic flux = AB

A: area = π r^2 = π (0.0415m)^2 = 5.41*10^-3 m^2

you replace the expression for the magnetic flux in the equation (1). Next, you derivative the magnetic field respect to time. Finally,  you replace t=5.00s:

(b) The current is given by:

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