The flux through a loop is given by phiB t t2 4t 101 Tm2

The flux through a loop is given by phi_B (t) = (t^2 - 4t) * 10^-1 Tm^2 where t is in seconds, Find the induced emf epsilon as a function of time, Find both phi_B and epsilon at t = 0, t = 2s, t = 4 s, and t = 6s. Sketch graphs of phi_B and epsilon versus t.

Solution

a) E= -d phi/dt = 4-2t

b) phi at 0 s = 0

at 2 s = (2*2-4*2 ) * 10^-1 Tm^2 = .4 Tm^2

at 4s = 0

at 6s = 1.2 Tm^2

E(0) = 4 V

E(2) = 0

E(4) = -4 V

E(6) = -8 V