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Assign2 - PHY 54 Assignment 2 Summer 2011 Reading...

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Reading : Electrostatics 2. Key concepts: Electrostatic potential, conductors as equipotentials, calculating V by superposition and from E , torque on a dipole, electrostatic potential energy. 1. Questions about the relations between E and V in electrostatics. a. If E is uniform and in the x -direction, i.e., E = E i , where E is constant, what is V ( x ) , choosing V (0) = V 0 ? b. If V is constant, what is E ? c. Show from the definition of V in terms of E that if one moves parallel to the E-field the potential decreases. d. As one moves along the surface of a conductor the potential does not change. Does this mean that E has the same value at all points? Explain. 2. Shown are two situations involving point charges at fixed positions on the x -axis. Take V ( ) = 0 for point charges. In each case: a. Is there a point on the axis where the total potential is zero? If so, where (left of both, between them, right of both)? b. Answer the same question for the total E-field of the charges. (Specify all such points if there is more than one.) 3. An electron (charge – e ) is released from rest in the vicinity of other charges. a. Does it move toward higher or lower potential? b. Does it move toward higher or lower potential energy? c. Does it move parallel or opposite to E ? 4. Shown are lines of constant potential, each line 5 V lower than the one to its left. a. What is the direction of the E-field? How do you know? b. Is the magnitude of E increasing to the right? To the left? Not changing? 5. Questions about field lines. a. Can lines of the E-field cross each other? Explain. b. Can lines of equal potential cross each other? Explain. + q 3 q + q + 3 q ( a ) ( b ) 20 0 PHY 54 Assignment 2 Summer 2011
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6. “Grounding” means connecting a conductor to the earth, a very large conductor which can accept or supply significant amounts of charge without changing its potential — which one usually chooses to be zero. “Shielding” means surrounding a region of space by a grounded conductor. Some examples: a. An uncharged conducting spherical shell surrounds a point charge as q shown. Charge q appears on the outer surface of the shell. (Why?) What are the E-field and potential outside the shell? Does it matter whether the point charge is at the center of the shell’s cavity?
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