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1 Physics 2080 Final Exam Problems Due April 28, 2011 Instructions: This is part of the final exam. Books and notes are allowed, but all work should be YOUR OWN. Do not work in groups; every student should turn in their own solutions. Print this exam and write on it. Do NOT turn in notebook paper or solutions on anything other than this exam. Make sure you put your name, show all work in a neat and organized manner, explain your reasoning where appropriate, and circle your answer. 1. Bulbs of fixed resistance 3.0 Ω and 6.0 Ω, a 9.0 V battery, and a switch S are connected as shown. The switch S is closed. a. Calculate the current in bulb A. b. Which bulb is brightest? Justify your answer. c. Switch S is then opened. For each bulb, indicate whether the brightness of the bulb increases, decreases, or remains the same. Explain your reasoning for each bulb. i. Bulb A: ii. Bulb B: iii. Bulb C:

2 2. A proton of mass m p and charge e is in a box that contains an electric field E and the box is located in Earth s magnetic field B. The proton moves with an initial velocity vertically upward from the surface of Earth. Assume gravity is negligible. a. On the diagram above, indicate the direction of the electric field inside the box so that there is no change in the trajectory of the proton while it moves upward in the box (i.e., what electric field is necessary so that the proton moves vertically upward without being deflected while in the box). Explain your reasoning. b. Determine the speed of the proton while in the box if it continues to move vertically upward. Express your answer in terms of the fields and the given quantities. The proton now exits the box through the opening at the top. c. On the diagram above, sketch the path of the proton after it leaves the box. d. Determine the magnitude of the acceleration a of the proton just after it leaves the box, in terms of the given quantities and fundamental constants.

3 3. Four charged particles are held fixed at the corners of a square of side s. All the charges have the same magnitude Q, but two are positive and two are negative. In arrangement 1, shown, charges of the same side are at opposite corners. Express your answers to parts a and b in terms of the given quantities and fundamental constants. a. For arrangement 1, determine the following: i. the electrostatic potential at the center of the square ii. the magnitude of the electric field at the center of the square The bottom two charged particles are now switched to form arrangement 2, shown, in which the positively charged particles are on the left and the negatively charged particles are on the right. b. For arrangement 2, determine the following: i. the electrostatic potential at the center of the square ii. the magnitude of the electric field at the center of the square c. In which of the two arrangements would more work be required to remove the particle at the upper right corner from its present position to a distance a long way away from the arrangement? Justify your answer.

4 4. Two parallel conducting plates, each of area 0.30 m 2, are separated by a distance of 2.0 cm of air. One plate has a charge +Q and the other has a charge Q. An electric field of 5000 N/C is directed to the left in the space between the plates, as shown. a. Indicate on the diagram which plate is positive and which is negative. b. Determine the potential difference between the plates. c. Determine the capacitance of this arrangement of plates. An electron is initially located at a point midway between the plates. d. Determine the magnitude of the electrostatic force on the electron at this location and state its direction. e. If the electron is released from rest at this location midway between the plates, determine its speed just before striking one of the plates. Assume that gravitational effects are negligible.

5 5. Three identical resistors, each of resistance 30Ω are connected in a circuit to heat water in a glass beaker. A 24 V battery with negligible internal resistance provides the power. a. The three resistors may be connected in series or in parallel. i. If they are connected in series, what power is developed in the circuit? ii. If they are connected in parallel, what power is developed in the circuit? b. Using the battery and one or more of the resistors, design a circuit that will heat the water at the fastest rate when the resistor(s) are placed in the water. Include an ammeter to measure the current in the circuit and a voltmeter to measure the total potential difference of the circuit. Assume the wires are insulated and have no resistance. Draw a diagram of the circuit in the box below, using the following symbols to represent the components in your diagram.

6 6. An object is placed 30 mm in front of a lens. An image of the object is located 90 mm behind the lens. a. Is the lens converging or diverging? Explain your reasoning b. What is the focal length of the lens? c. On the axis below, draw the lens at position x = 0. Draw at least two rays and located the image to show the situation described above. d. Based on your diagram in (c), describe the image by answering the following questions in the blank spaces provided. Is the image real or virtual? Is the image smaller than, larger than, or the same size as the object? Is the image inverted or upright compared to the object? e. The lens is replaced by a concave mirror of focal length 20 mm. On the axis below, draw the mirror at position x = 0 so that a real image is formed. Draw at least two rays and locate the image to show this situation. Describe the characteristics of the image (real or virtual, upright or inverted, enlarged or reduced).

7 7. Light consisting of two wavelengths, 440 nm and 550 nm, is incident normally on a barrier with two slits separated by a distance d. The intensity distribution (pattern of dark and bright fringes) is measured along a plane that is a distance L = 0.85 m from the slits as shown above. The movable detector contains a photoelectric cell whose position y is measured from the central maximum. The first order maximum for the longer wavelength occurs at y =1.2 cm. a. Determine the slit separation d. b. At what position Y does the first order maximum occur for the shorter wavelength? In a different experiment, light containing many wavelengths is incident on the slits. It is found that the photosensitive surface in the detector is insensitive to light with wavelengths longer than 600 nm. c. Determine the work function of the photosensitive surface. d. Determine the maximum kinetic energy of electrons ejected from the photosensitive surface when exposed to light of wavelength 440 nm.

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