Physics 2A03 Assignment #8 : Induction/LC

1) A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 2.50 T in 1.00 s. What is the resulting induced current if the loop has a resistance of 2.00 Ω?

2) A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown below.

a) Determine the magnetic flux through the loop due to the current I. (Hint: B is not constant across the loop!). b) Suppose the current is changing according to I = a + bt, where a and b are constants. Determine the emf induced in the loop if b = 10.0 A/s, h = 1.00 cm, w = 10.0 cm, and L = 100 cm. What is the direction of the induced current?

3) The figure below shows a top view of a bar that can slide without friction. The resistor is 6.00 Ω and a 2.50-T magnetic field is directed perpendicularly downward, into the paper. Let ℓ = 1.20 m.

a) Calculate the applied force required to move the bar to the right at a constant speed of 2.00 m/s. b) At what rate is energy delivered to the resistor? 4) The current in a 90.0-mH inductor changes with time as I = 1.00t2 – 6.00t (in SI units). Find the magnitude of the induced emf at a) t = 1.00 s b) t = 4.00 s c) At what time is the emf zero?

5) When the switch in the figure below is closed, the current takes 3.00 ms to reach 98.0% of its final value. If R = 10.0 Ω, what is the inductance?

6) A series RL circuit with L = 3.00 H and a series RC circuit with C = 3.00 μF have equal time constants. If the two circuits contain the same resistance R, a) what is the value of R and b) what is the time constant?