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CU-Boulder PHYS 1120 - EM Waves problems w/key

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1 of 7 CTEM-1. Which has higher frequency? A) Red light B) Violet-blue light C) Same frequency D) Depends on how the light is made Answer: Red light has longer wavelength (λ = 700 nm). Violet-blue light has shorter wavelength λ (λ = 400 nm), and therefore higher frequency f. λ f = constant = c, so if λ is smaller, f must be higher. CTEM-2. An EM plane wave is described by 00ˆˆE E sin(kz t)x, B B sin(kz t)yωω= − = −KK E (x) Consider 3 antennas, labeled 1, 2, and 3. Antenna 1 is on the z axis. Antenna 2 is in the xz plane, above 1. Antenna 3 is is off the z-axis at the location shown. Rank the antennas by average signal strength received, from largest to smallest: A) 1 > 2 > 3 B) 1=2=3 C) 1 = 2 > 3 Answer: 1=2=3 c (z)B (y)123Phys1120 Concept Tests, M.Dubson ©University of Colorado at Boulder2 of 7 CTEM-3. A point source of radiation emits power Po isotropically (in all directions uniformly). A detector of area ad is located a distance R away from the source. What is the power p received by the detector? A: PRaod42π B: PaRod22 Rdetector adC: PaRod Po D: PRaodπ2 E: None of these. Answer: power received = (power/area) × (receiver area) = intensity× (receiver area) = PRaod42π CTEM-4. Two radio dishes (shaped like bowls) are receiving signals from a radio station which is sending out radio waves in all directions with power P. Dish 2 is twice as far away as Dish 1, but has twice the diameter. Which dish receives more power? (Dish 2 is not in the shadow of Dish 1.) A: Dish 1 B: Dish 2 C: Both receive the same power Dish 1Dish 2 Answer: Both receive the same power. Dish 2 has four times the area (2 times the diameter). But dish 2 is twice as far away so it receive ¼ the power per area as dish 1. Phys1120 Concept Tests, M.Dubson ©University of Colorado at Boulder3 of 7 Remember: intensity = power per area is proportional to 1/R2, so if R doubles, R2 increases by a factor of 4. The power received is given by the formula in the previous concept test: PRaod42π. For dish 2, ad = detector area is 4 times as large as dish 1. Notice that the dotted lines in the diagram above so that dish 1 and dish 2 both cover the same fraction of a big sphere centered on the transmitting tower. So dish 1 and dish 2 both receive the same fraction of the total energy coming from the tower. CTEM-5. A parabolic dish focuses the EM radiation from a source into a beam of constant diameter D : DcR The intensity of the light in the beam falls with distance R as: A) 21IR∝ B) 1IR∝ C) 01I constantR∝ = D) Something else. Answer: 01I constantR∝ = Phys1120 Concept Tests, M.Dubson ©University of Colorado at Boulder4 of 7 CTEM-6. Light from a source is partially focused so that it diverges from the source uniformly over a cone of angle 200. c The intensity of the light in the beam falls with distance R as: A) 21IR∝ B) N1I,NR∝ > 2 C) N1I,NR∝ < 2 D) 01IR∝ D) Something else. constant= Answer: 21IR∝. The cone is a constant fraction of a sphere. CTEM-7. A polarized beam of light passes through three ideal polaroid filters. The filters, in order 1st, 2nd, 3rd, are tilted at 0o, 45o, and 90o with respect to the incoming beam's axis. Does any light get through the all the filters and come out the other side? A: Some light gets through. B: No light gets through. θ = 200 RE c Phys1120 Concept Tests, M.Dubson ©University of Colorado at Boulder5 of 7 Answer: some light gets through. If the 2nd filter were not present, then no light would get thru. After the first filter, the E-field is unchanged, E1=Eo. After the 2nd filter the E-field is E2 = Eo cos(45o) . After the third filter the E-field is E3 = E2 cos(45o)= Eo cos(45o) cos(45o) = Eo/2. The intensity of the light (intensity I = S ) is proportional to the E2, so the final intensity is Io/4. CTEM-8.An unpolarized beam of light passes through 2 polaroid filters oriented at 45o with respect to each other. The intensity of the original beam is Io. What is the intensity of the light coming through both filters? (Hints: cos45o = 1/2. The average of cos2θ, average over all values of θ, is cos /212θ= .) A: (1/2)Io Io c B: (1/4)Io C: (1/8)Io D: (1/16)Io E: None Answer: (1/4)Io After the first filter, the intensity is I1 = Io(1/2). Reason: If the original beam were polarized, then after passing through one filter the intensity would be I1 = Io cos2θ , but here the original beam is unpolarized so all angles θ are in the beam. The intensity after one filter is then I1 = Io (cos2θ)average = Io(1/2). After the second filter the intensity is I2 = I1 cos245 = I1 (1/2) = Io(1/2)(1/2) = Io(1/4). CTEM-9. Under cover of night, a Girl scout signals her friends on a distant hill by alternately placing slabs of red or green Jell-O over her flashlight. This signal is most accurately described as.. A: Frequency modulation. B: Amplitude modulation. Answer: When the Girl scout signals by changing the color of the light (keeping the brightness fixed), this would be frequency modulation, because different frequencies of visible light correspond to different colors. Phys1120 Concept Tests, M.Dubson ©University of Colorado at Boulder6 of 7 If the scout signals by alternately dimming and brightening the bulb, then that would be amplitude modulation. The brightness of the light is a measure of the amplitude of the electric field in the E/M waves from the light. AM FM dim bright less bright CTEM-10. A row of positive charges is stationary on the ground. A person with a of oes the person measure a non-zero B-field? gauss-meter (which measures the magnetic field) is running to the right along the rowcharges, at the same height as the charges and in front of them (in the diagram below). DA) Yes B) No Answer: Yes. In the frame of reference of the moving person, the positive charges are moving to the left. From the person point of view, the positive charges constitute a current to the left. Currents make B-fields. What is the direction of the B-field which the moving observer measures? c ard direction ← ro A) Up↑ B) Down↓ C) Forward direction → D) ba kwE) no direction, B-field ze vPhys1120 Concept Tests, M.Dubson ©University of Colorado at Boulder7 of 7 Answer: Upward. Note that the person is in front of the wire, not above or below the wire. I B Phys1120


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