Question

1. The electric circuit in the diagram on the left, below, consists of a wire (without resistance) and a 5.0 2 resistor. Current is driven through the circuit by a changing magnetic field that fills the area inside of the circuit and points into the paper, as shown Magnetic field as a function of time T o ® ® ® 40.0 cm Magnetic field in tesla 0.02 Time in seconds 0.C 0.01 0.03 70.0 cm The external magnetic field points into the plane of the paper and the magnitude is given by: B(t) = (0.700 T) - Bext sin(wt) Where w = 70.0 rad/s and Bext = 0.500 T a) In the circuit diagram above, draw an arrow to show the direction of the current induced in the resistor at the time = 0.0100 seconds. In the space below, sketch a graph of the current induced in the resistor as a function of time. The current is positive when it is moving up through the resistor (clockwise around the loop). The shape of the graph is important. Exact numbers are not. Time in seconds 0.03

Answer 1

a) At t = 0.01 s, the magnetic field is decreasing and it is into the page. Therefore the induced current will be in such a direction that it increases the magnetic field pointing into the page. Hence the direction of the induced current will be CLOCKWISE in the circuit or the direction will be up through the resistor.

b) The magnetic field is

B = 0.7 -0.5 sin(700)

The current through the circuit is

I= AB=5 Rat Ad. 0.4 x 0.7 -- x 35. cos(70t) = 1.96 cos(700)

c) The current at t = 0.0183 s is

I = 1.96 cos(70 x 0.0183) = 0.56 A