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Ch0205 - Chapter 5 Work Done by the Electric Field and the...

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Chapter 5 Work Done by the Electric Field, and, the Electric Potential 32 5 Work Done by the Electric Field, and, the Electric Potential When a charged particle moves from one position in an electric field to another position in that same electric field, the electric field does work on the particle. The work done is conservative; hence, we can define a potential energy for the case of the force exerted by an electric field. This allows us to use the concepts of work, energy, and the conservation of energy, in the analysis of physical processes involving charged particles and electric fields. We have defined the work done on a particle by a force, to be the force-along-the-path times the length of the path, with the stipulation that when the component of the force along the path is different on different segments of the path, one has to divide up the path into segments on each of which the force-along-the-path has one value for the whole segment, calculate the work done on each segment, and add up the results. Let’s investigate the work done by the electric field on a charged particle as it moves in the electric field in the rather simple case of a uniform electric field. For instance, let’s calculate the work done on a positively-charged particle of charge q as it moves from point P 1 to point P 3 along the path: “From P 1 straight to point P 2 and from there, straight to P 3 .” Note that we are not told what it is that makes the particle move. We don’t care about that in this problem. Perhaps the charged particle is on the end of a quartz rod (quartz is a good insulator) and a person who is holding the rod by the other end moves the rod so the charged particle moves as specified. b a E P 2 P 3 P 1 c
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Chapter 5 Work Done by the Electric Field, and, the Electric Potential 33 Along the first part of the path, from P 1 to P 2 , the force on the charged particle is perpendicular to the path. The force has no component along the path so it does no work on the charged particle at all as the charged particle moves from point P 1 to point P 2 . 0 12 = W From P 2 , the particle goes straight to P 3 . b a E P 2 P 3 P 1 c F
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Chapter 5 Work Done by the Electric Field, and, the Electric Potential 34 On that segment of the path (from P 2 to P 3 ) the force is in exactly the same direction as the direction in which the particle is going. As such, the work is just the magnitude of the force times the length of the path segment: b F = 23 W The magnitude of the force is the charge of the particle times the magnitude of the electric field F = q E , so, b E q = 23 W Thus, the work done on the charged particle by the electric field, as the particle moves from point P 1 to P 3 along the specified path is 23 12 123 W W W + = b E q + = 0 123 W b a E P 2 P 3 P 1 c F b E q = 123 W (This is just an answer to a sample problem. Don’t use it as a starting point for the solution to a homework or test problem.)
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Chapter 5 Work Done by the Electric Field, and, the Electric Potential 35
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