In the figure the magnetic flux through the loop increases a

In the figure, the magnetic flux through the loop increases according to the relation Phi_B = 5.6t^2 + 9.7t, where Phi_B is in milliwebers and t is in seconds. What is the magnitude of the emf induced in the loop when t =1.8 s? Is the direction of the current through R to the right or left?

Solution

a) Flux _B = 5.6t² + 9.7t

= d_B/dt =11.2t + 9.7

at t= 2 sec,   = d_B/dt =11.2x2+9.7=32.1 mV

b) The flux is pointing out of the paper and rising. The coil reacts to oppose this rising outward field by generating a field that points into the paper. To do this, the current must flow to the left through the resistor.