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Exam1_2007Spr_Solutions

# Exam1_2007Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2007 8.02 Exam One Spring 2007 Solutions SECTION I In this section you are asked to answer 5 questions, each worth 5 points. You do not have to show your work; in most cases you may simply circle the chosen answer. Question 1 (5 points): A parallel plate capacitor has a voltage difference V applied between the two plates. If the voltage difference is increased to 2 V , the energy stored in the capacitor: (a) will increase by a factor of two. (b) will decrease by a factor of two. (c) will increase by a factor of four. (d) will decrease by a factor of four. (e) will not change. Answer: (c). The stored potential energy is proportional to the square of the potential difference, . Thus doubling the potential difference increases the stored energy by a factor of 4. 2 (1/ 2) UC =∆ V 1

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Question 2 (5 points): Consider the equipotential and electric field lines shown in the figure below associated with a charged conducting disk. Which of the following is true? Multiple answers are possible. (a) The magnitude of the electric field is largest on the surface of the disk at the center of the disk. (b) The magnitude of the electric field is largest on the surface of the disk at either end (c) Along a line passing through the center of the disk, the electric field points away from the center of the disk. (d) Along a line passing through the center of the disk, the electric field points toward the center of the disk. (e) The direction of the electric field cannot be determined from the information given. Answer: (b) and (e). The electric field is strongest at the edges of the disc where the electric potential is changing most rapidly. Since we don’t know where is positive or negative we cannot tell whether the potential decreases or increase as you move away from the center of the disk, along a line passing through the center of the disk. Hence the direction of the electric field cannot be determined from the information given. 0 V 2
Question 3 (5 points): Consider two spherical hollow conductors, as shown in the diagram below. A point charge + Q is placed in the center of the conductors. If a wire is used to connect the two conductors, then positive charge will flow: (a) From the outer to the inner conductor.

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Exam1_2007Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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