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Unformatted text preview: Physics 2Ba quiz 3 solutions (Dated: January 31, 2009 2:31) Problem 1 Electric field lines go from region A to region B. We must conclude that A) The electric potential in region A is positive while the electric potential in region B is negative B) The electric potential in region B is positive while the electric potential in region A is negative C) The electric potential is everywhere positive and larger in region A than in region B D) The electric potential is everywhere positive and larger in region B than in region A E) None of the above The correct answer is E . The change in potential, V is given by the following formula. V =- Z B A E d r (1) Since the electric field lines point from B to A , if we choose a straight integration path between the two points, then the dot product E d r is positive since the electric field points from A to B (cos = 1). The integral will always be positive and so we must conclude from Eq. (1) that V is negative. However, we only know the change in potential from A to B , we do not know the absolute potential. There is not enough information, since in order to determine whether the potential is positive or negative, we must be told something about the absolute potential at A or B . Problem 2 The figure below shows equipotentials surrounding a pair of charges Q A and Q B . The value of the potential half-way between the charges is indicated. Which of the statements below applies to the charges? A) The two charges have opposite signs and equal magnitudes. B) Nothing can be said about the charges. C) The two charges have the same sign and equal magnitudes. D) The two charges have the same sign but there is not enough information to compare their magnitudes. E) The two charges have opposite signs but there isnt enough information to compare their magnitudes. The correct answer is A . The symmetry of the diagram tell us that the charges must have equal magnitude. If the charges had the same sign, the potential would not be zero anywhere except possibly at r = . The fact that there exists an equipotential line with V = 0, we know that along this line the contribution from each charge must cancel against each other; therefore, the charges have opposite sign. Also, any point on the V = 0 line has the same distance to each charge, and so again we are forced to conclude the charges have equal magnitude. 2...
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This note was uploaded on 03/28/2009 for the course PHYS 2b taught by Professor Schuller during the Winter '08 term at UCSD.
- Winter '08
- Electric Potential