Study Problems – Inductance and Electromagnetic Waves - Solutions
Question 1 (1 point)
What is Lenz’s Law? To which basic principle of physics is it most closely related?
Solution: Lenz’s law states that the induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop. It is closely related to conservation of energy.
Question 2 (3 points)
The rotating loop in an AC generator is a square 25 cm on each side with 320 turns of wire in the loop. It is rotated at 60 Hz in a uniform field of 0.45 T. Calculate the magnitude of the emf induced in the loop as a function of time.
Solution: EMF (E) = NABω * (sin ωt)
= 320 (.25 m)^2 * (0.45T) (2πf) sin (2πft)
= 1080π m^2 * T * Hz * sin(120π Hz * t)
= 3390 V sin (377Hz * t)
Question 3 (3 points)
An electromagnetic plane wave at a certain location has an electric field pointed up which is given as a function of time as E = 54 V/m × sin (6x106 Hz × t). The magnetic field at the same location points south when the electric field points up. What is the maximum intensity of the wave? In what direction does it travel? What is its wavelength?
E = 54 V/m X sin(6 X 106 Hz X t ) up
S = E X B / μ0 (towards the east)
S = |E| * |E| / c * μ0
= [((54 v/m)2) * (sin2(6 X 102 Hz x t))] / [(4π X 10-7 Tm/A) (3 X 108 m/s)]
= 7.7 sin2 (6 X 106 Hz X t) w/m2 (towards the east)
v = λf = c
λ = c/f = 2π c /ω = [2π X (3 x 108 m/s)] / [6 X 106 Hz] = 314 m
Question 4 (3 points)
The wave in question 3 is incident on a square piece of foil which is 3.6 m long on each side. If the wave is completely absorbed by the foil for 35 seconds, how much energy does the foil absorb? Assume the foil is set up in the south-up plane.
S(average) = I = P (average) / Area = (Energy / Δt) / Area
Therefore à Energy = S (average) X Area X Δt
= [|E (max)|2 * A * Δt] / 2 *μ0* c
= [(54 V/m) 2 * (3.6 m)2 * (35 s) ] / [2 * (4π X 10-7 Tm/A) * (3 X 108 m/s)]
= 1750 J