#### A Point Charge vs. a Line of Charge

Consider the electric field at a point some distance from, and directly above, a point charge Q. What happens to the field at the point if the point charge is spread uniformly over a horizontal line, as shown? In which case is the field larger?

1. the field is larger when the charge is concentrated into one point
2. the field is larger when the charge is spread over the line
3. the field is the same in both cases

The field is larger when the charge is concentrated at a single point, for two reasons. First, when the charge is distributed over the line it is generally further away from the point than the point charge was - this reduces the magnitude of the field. Second, the electric fields from the different parts of the line don't point in the same direction. When you add them as vectors to get the net field there's some cancellation.

This might be easier to see if you think of the line of charge as being made up of charges in a line.
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