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Unformatted text preview: Physics 204, summer 2008 Exam #2 practice problems 1. A current flows upward in a long straight wire. To the right is a rectangular loop that is also carrying a current (the power supply is not shown so the diagram doesn’t get too cluttered). Predict the magnetic force the straight wire exerts on the rectangular loop. 2. Two long straight wires are carrying currents in opposite directions as shown in the diagram. a. Predict the magnitude and direction of the magnetic field at each of the 3 points shown. b. Will the wires be attracted to each other, repelled by each other, or not exert a force on each other at all? Explain in detail the reasoning behind your choice. 3. Two parallel wires are carrying currents as shown in the diagram. The electrons that make up the current I 2 move at a very slow average speed, in this case approximately 6.9 × 10−5 m s . a. Draw a picture of the magnetic field generated by I1 . I 2 = 3.00 A I1 = 2.00 A b. What is the magnitude and direction of the magnetic force, if any, that is exerted on one of the moving electrons in the wire on the right. 10.0cm 4. Imagine that a space mission has been planned to send a probe to the planet Mercury. One of the goals of the mission is to measure the magnetic field of the planet as a function of altitude above the north magnetic pole of the planet. To do this, the space probe is being designed with a ring made of 1000 turns of conducting wire. This ring has a radius of 2.00m and a total resistance of 10.0Ω . As the probe descends this ring will be kept parallel to the surface of the planet. You estimate that the probe will take 300 seconds to descend from orbit (where the magnetic field is zero) to the surface (where the magnetic field has an approximate magnitude of 10 −5 T ). Predict the current that will flow in the ring as the probe descends to the surface. 5. A square loop of wire (of negligible resistance) is connected to a light bulb that has a resistance of 10.0Ω . The magnetic field within the loop is uniform and points perpendicular to the plane of the loop. A graph of the magnetic field is shown (positive values mean the magnetic field points out of the page.) Draw a graph showing the current flowing through the light bulb as a function of time. When there is a current, if ever, predict its value and direction. 6. You are at a bowling alley picking out the ball you are going to use when you see a highly polished silver colored ball. When you reach down to pick it up you see an image of yourself created by its shiny surface. a. Qualitatively, where is this image located and what are its properties (magnified/demagnified, upright/inverted, etc.)? Include a ray diagram to support your answers. b. If the radius of the ball is 15.0cm and your face is 35.0cm from the surface of the ball, numerically determine the location and magnification of the image. 7. In the future it is possible that particle beams might be used as weapons in space combat. A magnetic field could be used deflect such beams. You decide to set up an experiment to test this idea. In your experiment the incoming particle beam consists of protons traveling at 1.00% of the speed of light. They are traveling toward a region (between the two dashed lines) where the magnetic field is not zero, as shown in the diagram. You set up a uniform magnetic field with a magnitude of 10 Tesla between the two dashed lines. If this “magnetic shield” works the protons will never cross the second dashed line B=0 B≠0 B=0 v a. Assuming the shield works, draw a picture showing carefully the trajectory of the protons. Also show the direction of the magnetic field that will cause the protons to move in this way. b. How wide would the region with the magnetic field have to be so that it acts as an effective shield? Or to put it another way, what is the minimum distance between the two dashed lines? (Hint: Assume the protons just barely get turned around by the time they reach the second dashed line.) 8. You are a safety inspector hired by the Princeton Plasma Physics Laboratory to determine if their new experimental nuclear fusion reactor is generating too strong a magnetic field in nearby offices. You go to the office nearest the experiment which turns out to be directly above the main fusion reactor. The scientists who designed the reactor tell you that the device will create a magnetic field in the office that points directly upward and will have approximately the same strength everywhere in the room. You take out a circular loop of wire (radius 0.500m , resistance 0.200Ω ) and orient it so the plane of the coil is parallel to the floor. You connect the coil to an ammeter as shown in the diagram. When the nuclear fusion reactor is turned on the ammeter deflects to the right 1 and reads a value of 0.600mA for 2.00s a. Were the scientists correct about the direction of the magnetic field? Explain your reasoning. b. Estimate the magnitude of the magnetic field in the office. 9. You are looking straight down into a large polished metal bowl sitting on the table in front of you. When you look into the bowl you see an inverted image of yourself. As you bring your face closer to the bowl you notice that at a distance of about 40.0cm the image of your face flips over and becomes upright. a. Draw a ray diagram showing the image that is formed when your face is 100cm away from the bottom of the bowl. Predict the image distance and the image magnification. b. Draw a ray diagram showing the image that is formed when your face is 30.0cm away from the bottom of the bowl. Predict the image distance and the image magnification. 10. High voltage power lines are often seen suspended high above the ground. There are safety concerns regarding these power lines because of the magnetic fields they generate. Imagine that there are two of these power lines suspended 50.0m above you, and 15.0m apart from each other. Each carries an electric current of 10.0 A , but in opposite directions. You are standing on the ground beneath the two power lines, directly between them. • × a. Predict the magnitude of the force that each 100m of length that the power lines exert on each other. Is it an attractive or repulsive force? b. What is the direction of the magnetic field created by the two wires where you are standing? Draw a diagram illustrating your reasoning. c. Predict the magnitude of the magnetic field where you are standing. (Challenging: Only worth 2 of the 10 total points for this problem.) 11. Your friend has lost his glasses and can’t get a replacement until next week. Your dad is an eye doctor but he’s away at a conference. You know that your dad keeps a drawer full of old eyeglass frames and lenses that have been labeled with their focal lengths. Your friend explains that he has a rather complicated problem with his vision. He tells you that with his left eye he can’t focus on anything further away than 2.00m . With his right eye he can’t focus on anything closer than 7.00m . Since you’ve been studying optics in your physics course you think you can help by making him a pair of eyeglasses with what your dad has in his drawer. a. What type of lenses should the eyeglasses have and what should be their focal lengths? b. Draw a ray diagram for each lens illustrating why your choice for the lens will allow your friend to see normally. 1 The ammeter will deflect to the right when the current is flowing into the right terminal and will deflect to the left when the current is
flowing into the left terminal. 12. Several people living around Lake Fishstory claimed to have seen a large sea monster swimming near a shallow part of the lake last night. In order to find the monster the local police department sends a helicopter with a bright searchlight to the scene. The searchlight shines a cone of white light down on the surface of the lake as shown (the refractive index of the lake water varies from 1.34 for 400nm light to 1.32 for 700nm light). The lake water is calm and very clear. a. Draw a complete ray diagram for what happens to the light from the searchlight. 50° 15m 35m b. Describe mathematically the size and shape of the illuminated region at the bottom of the lake. If the illuminated region does not all appear the same color, be specific about what colors appear where. 13. A specially prepared beam of light is traveling in glass and is about to strike an interface with air as shown in the diagram. This beam of light is comprised of only two wavelengths, 600nm (orange), and 450nm (blue). If you had to choose an angle to fire the beam toward the interface with so that only one of these two colors will make it into the air, what angle would you choose? The air has an index of refraction of 1.00 and basically doesn’t depend on wavelength. The index of refraction of this glass varies linearly from 1.49 at 600nm to 1.50 at 450nm . Air θ Glass 14. People who do not need glasses have lenses in their eyes that are able to clearly focus objects (meaning they look sharp and not fuzzy) that are anywhere from 20.0cm to extremely far away from the eye (such as the stars in the night sky). a. This means that a healthy lens must be able to adjust its focal length. What range of focal lengths can it have? Hint: You will have to estimate at least 1 quantity to get a numerical answer to this. Make it reasonable. b. Someone who is nearsighted is not able to focus on distant objects. Imagine that you have a friend who is strongly nearsighted and cannot focus on anything further than 1.00m away. In order to correct this, glasses are needed that will take the light from very distant objects and create an image just 1.00m away. Describe the lens that will do this and determine its focal length. c. Draw a ray diagram showing the image this lens will create of a 20.0cm tall object that is 1.50m away from the lens. 15. Two underwater science stations are each located at a depth of 1200m on opposite sides of an underwater volcano that they are studying. The two stations cannot send signals directly to one another using electromagnetic waves through the water because the volcano is in the way. But, it might be possible for them to communicate by reflecting signals off the surface of the water above. Ocean water has an index of refraction of 1.33 . a. What phenomenon will allow the signals to reflect strongly off the undersurface of the water, and what circumstances allow this phenomenon to happen? b. What is the minimum horizontal distance that the two stations can be separated by so that this communication scheme will work? ...
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This note was uploaded on 10/04/2009 for the course PHYSICS 750:204 taught by Professor Croft during the Summer '08 term at Rutgers.
- Summer '08