Exam1_2010Spr_Solutions

Exam1_2010Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2010 8.02 Exam One Solutions Spring 2010 Problem 1 (25 points) Question 1 (5 points) 1. Above we show the grass seeds representation of the field of four point charges, located at the positions indicated by the numbers. Which statement is true about the signs of these charges: a) All four charges have the same sign. b) Charges 1 and 2 have the same sign, and that sign is opposite the sign of 3 and 4. c) Charges 1 and 3 have the same sign, and that sign is opposite the sign of 2 and 4. d) Charges 1 and 4 have the same sign, and that sign is opposite the sign of 2 and 3. e) None of the above. Solution b. Field lines continuously connect charges 1 and 3, and 2 and 4 respectively, indicating that the charge of those pairs are opposite in sign. The field is a zero between charges 1 and 2 indicating that they repel and hence are of the same sign. A smilar argument holds for charges 3 and 4.
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2 Question 2 (5 points) The grass seeds figure below shows the electric field of three charges with charges +1, +1, and -1, The Gaussian surface in the figure is a sphere containing two of the charges. The total electric flux through the spherical Gaussian surface is a) Positive b) Negative c) Zero d) Impossible to determine without more information Solution c. Because the field lines connect the two charges within the Gaussian surface they must have opposite sign. Therefore the charge enclosed in the Gaussian surface is zero. Hence the electric flux through the surface of the Gaussian surface is also zero.
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3 Question 3 (5 points) Two point-like charged objects with charges Q + and Q are placed on the bottom corners of a square of side a , as shown in the figure. You move an electron with charge e from the upper right corner marked A to the upper left corner marked B. Which of the following statements is true? a) You do a negative amount of work on the electron equal to the amount of energy necessary to assemble the system of three charged objects with the electron at point B. b) You do a positive amount of work on the electron equal to the amount of energy necessary to assemble the system of three charged objects with the electron at point B. c) You do a positive amount of work on the electron and the potential energy of the system of three charged objects increases. d) You do a negative amount of work on the electron and the potential energy of the system of three charged objects decreases. e) You do a negative amount of work on the electron and the potential energy of the system of three charged objects increases. f) You do a positive amount of work on the electron and the potential energy of the system of three charged objects decreases. Solution d. Because point B is closer to the positive charge than the point A, the electric potential difference () () 0 VB VA −> . When you move an electron with charge e from the upper right corner marked A to the upper left corner marked B, the potential energy d i f f e r e n c e i s () (() () ) 0 UB UA eVB VA −= < . This means that you do a negative
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This note was uploaded on 02/27/2011 for the course PHYSICS 8 taught by Professor Dourmashkin during the Fall '10 term at MIT.

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Exam1_2010Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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