3. epotsoln - H omework on Potential - Answers 1. An...

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Homework on Potential - Answers 1. An stationary electron is infinitely far from a proton. (remember the potential inifinitely far from a point charge is 0). What is its velocity when it falls to 5.3 x 10 -11 m? Use conservation of energy E i = E f K i + U i = K f + U f 0 + 0 = 1/2 m e v f 2 + q e V f [inital U = 0 by definition] V f = [1/4 π e o ] q p /r f subscripts e and p refer to electron and proton v f = {[-2/4 π m e e o ] q p /r f } 1/2 putting in values (don't forget sign of electron's charge!), we get v f = 3.1 x 10 6 m/s 2. Calculate the electric field of a point charge q' from the electric potential of the point charge. We need to take the gradient of the potential or, for r 1
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E ( r ) = - dV dr r from the lecture V ( r ) = q 4 π o r so E ( r ) = q 4 π o r 2 3. The potential at a distance z along the axis of a ring of radius R that has a charge Q uniformly distributed along its circumference is V ( z ) = Q 4 π o 1 ( z 2 + R 2 ) 1/2 Calculate the z component of the electric field. Same idea as previous problem, that is, take the derivative of V with respect to z (that is, get the gradient)
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3. epotsoln - H omework on Potential - Answers 1. An...

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