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Unformatted text preview: Exam No. 1 Solutions I. (20 pts) Three positive charges q 1 = +2 C, q 2 = +1 C, and q 3 = +1 C are arranged at the corners of an equilateral triangle of side 2 m as shown in the diagram. Calculate: a) The force exerted on q 1 by the other charges. Answer: Because charges q 2 and q 3 are equal, and q 1 lies on the line bisecting the two charges, the horizontal components will cancel, leaving only ti o p r the ver cal c m onents, o 4 cos 9 x 10 Nm C 1 x 10 C 2m cos 30 1.95 x 10 NC C 2 1.95 x 10 NC 2 x 10 . b) The electrostatic potential energy of the system of charges Answer: There are a number of ways to describe the potential energy associated with assembling a system of charges, 1 4 1 2 4 ,, 1 2 where V i is the potential at q i due to all the other charges, but the answers will all be the same. 1 For this assembly, 1 4 1 4 1 4 Since , this becomes 1 4 m C 9 x 10 N 2 22 x 10 C1 x 10 C 1 x 10 C1 x 10 C . c) A charge is now placed midway between q 2 and q 3 at point A. If the object is released from rest at this point, what is its velocity when it is a large distance from the three charges? (Take 9 x 10 ) Answer: This portion of the question requires recognizing that, far from the surface, the potential energy of a particle initially placed at position A will all be converted to kinetic energy, and the question is asking to solve for the velocity associated with that kinetic energy. The potential energy, U , that th ar wil av at A ill e U q 4 V , where V is the potential at A produced by th , the 4 ch ge l h e w b = e three positive charges, q 1 q 2 and q 3 . q 4 4 q q 4 3 x 10 C9 x 10 Nm C 2 x 10 C 3 2m cos 0 1 x 10 C 1m 1 x 10 C 1m . The loss of this potential energy will result in a gain in kinetic energy, so that far from the...
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