A circular coil with N turns of wire lies in the plane of the screen (the x-y plane). It has radius r and total resistance R. The uniform (but not constant) magnetic field in this region has two non-zero components given by: B, = c sin (2rt) and = at³ – bt where B is in Tesla if t is in seconds. a) Write an expression for the flux of the magnetic field through this coil as a function of time t. b) Write an expression for the emf induced in the coil of wire as a function of timet. c) What is the magnitude and direction of the current induced in the wire at time t= 4.00 s? Use the values: N = 3,348, r = 0.115 m, R = 15.0N, a = 4.54 mT/s³, b = 45.36 mT/s, and c = 1.01 mT. Note: "mT" stands for milli-Tesla.

A circular coil with N turns of wire lies in the plane of the screen (the x-y plane). It has radius r and total resistance R. The uniform (but not constant) magnetic field in this region has two non-zero components given by: B, = c sin (2rt) and = at³ – bt where B is in Tesla if t is in seconds. a) Write an expression for the flux of the magnetic field through this coil as a function of time t. b) Write an expression for the emf induced in the coil of wire as a function of timet. c) What is the magnitude and direction of the current induced in the wire at time t= 4.00 s? Use the values: N = 3,348, r = 0.115 m, R = 15.0N, a = 4.54 mT/s³, b = 45.36 mT/s, and c = 1.01 mT. Note: "mT" stands for milli-Tesla.