Question
Sketch the electric field lines in the vicinity of the conductor in Figure 18.47 given the field was originally uniform and parallel to the object's long axis. Is the resulting field small near the long side of the object?
Final Answer
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Solution video
OpenStax College Physics, Chapter 18, Problem 37 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. These field lines which were originally parallel and all to the right suppose will be bent by the presence of this conductor because the field lines will move the charges around in this conductor and make it polarized. So with the field lines moving to the right, they point in the direction of a force that would be applied on a positive charge which is the opposite direction to the force applied on a negative charge which is to say that the negative charge is from this end get yanked over here and so then they build up on this side. And then they leave behind these atoms that were originally neutral but now are missing some electrons that have gone over here and so these atoms on this side of the conductor are positively charged. And the field lines... the ones that are near the top here along this long side will be pulling some negative charges towards them and in doing so will end up going towards the conductor because this negative charge that's here would tend to attract a positive test charge that would be placed there. The field lines are always pointing in the direction of force that a positive test charge would experience if it was put there. So a positive test charge here would tend to be pushed not only to the right but also somewhat upwards due to the positive charge that's repelling it on this end of the conductor and so force would be in this sort of direction which is why this field line has this curve to it instead of just being straight across; there's a certain vertical component to the force a test charge would experience and so that's why there's this curve. Okay! And is the resulting field small near the long side of the object and the answer is 'Yes' because the density of the field lines is small here— it's lot of space between field lines— and so that says that the field strength is small whereas at the ends, the field lines are densely packed together which is a way of indicating that the field is strong at the ends.