HW3-Solutions

# HW3-Solutions - Version PREVIEW HW3 feng(58230 This...

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Version PREVIEW – HW3 – feng – (58230) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – Fnd all choices before answering. Potential Energy and Potential 01 001 10.0 points Assume we are given an electric Feld set up by an unknown charge distribution. U 0 is the amount of work needed to bring a point charge of charge q 0 in from inFnity to a point P . If the charge q 0 is returned to inFnity, how much work would it take to bring a new charge of 4 q 0 from inFnity to point P ? 1. U 0 2 2. U 0 8 3. 4 U 0 correct 4. U 0 4 5. More information is needed. 6. The correct answer is not given. 7. 0 8. U 0 9. 2 U 0 10. 8 U 0 Explanation: With the zero of potential energy and elec- tric potential set at zero, the potential V at a point P is V = U q U = V q , where U is the work needed to bring a charge q from inFnity to point P . Initially V = U 0 q 0 . To bring a charge of q = 4 q 0 in from inFnity requires U = V q = U 0 q 0 4 q 0 = 4 U 0 . Electrostatic Work 002 10.0 points The two charges Q are Fxed at the vertices of an equilateral triangle with sides of length a as shown. a a a Q Q q The work required to move a charge q from the other vertex to the center of the line join- ing the Fxed charges is 1. W = 0 2. W = 2 k Qq a 3. W = 6 k Qq a 4. W = 4 k Qq a 5. W = k Qq a 6. W = 2 k Qq a correct Explanation: U 1 = + k Qq a + k Qq a = +2 k Qq a U 2 = + k Qq a 2 + k Qq a 2 = +4 k Qq a W = U 2 U 1 = 2 k Qq a . Potential from Field 003 10.0 points If the potential in a region is given by the function V = 2 x y 2 cos( z ) , what is the y -component of the electric Feld at the point P = ( x ,y ,z )?

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Version PREVIEW – HW3 – feng – (58230) 2 1. E y = 2 y correct 2. E y = 2 x 3. E y = sin( z ) 4. E y = x 2 4 5. E y = y 3 3 6. E y = sin( z ) 7. E y = y 2 8. E y = 2 y 9. E y = cos( z ) 10. E y = 2 Explanation: The electric Feld is the gradient of the po- tential, so the y -component of the E -Feld eval- uated at P is E y = ∂ V ∂y = ∂y b 2 x y 2 cos( x ) B = [ 2 y ] = 2 y . Potential Diagrams 02 004 (part 1 of 4) 10.0 points Consider a sphere with radius R and charge Q Q and the following graphs: Q . r R 0 1 r 2 1 r M . r R 0 1 r Y . r R 0 1 r X . r R 0 1 r 2 P . r R 0 1 r 2 L . r R 0 1 r 2
Version PREVIEW – HW3 – feng – (58230) 3 G . r R 0 1 r 2 S . r R 0 1 r Z . r R 0 1 r Which diagram describes the electric Feld vs radial distance [ E ( r ) function] for a con- ducting sphere? 1. S 2. Z 3. G 4. P correct 5. L 6. Q 7. X 8. Y 9. M Explanation: The electric feld For R < r with the sphere conducting and/or uniFormly non-conducting: Because the charge distri- bution is spherically symmetric, we select a spherical gaussian surface of radius R < r , concentric with the conducting sphere. The electric Feld due to the conducting sphere is directed radially outward by symmetry and is therefore normal to the surface at every point.

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HW3-Solutions - Version PREVIEW HW3 feng(58230 This...

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