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## Example 3.3: Electric field generated by two point charges Question: Two point charges, and , are separated by a distance . What is the electric field at a point halfway between the charges? What force would be exerted on a third charge placed at this point? Take , , , and m.

Solution: Suppose that the line from to runs along the -axis. It is clear, from Coulomb's law, that the electrostatic force exerted on any charge placed on this line is parallel to the -axis. Thus, the electric field at any point along this line must also be aligned along the -axis. Let the -coordinates of charges and be and , respectively. It follows that the origin ( ) lies halfway between the two charges. The electric field generated by charge at the origin is given by The field is positive because it is directed along the -axis (i.e., from charge towards the origin). The electric field generated by charge at the origin is given by The field is negative because it is directed along the -axis (i.e., from charge towards the origin). The resultant field at the origin is the algebraic sum of and (since all fields are directed along the -axis). Thus, Since is negative, the resultant field is directed along the -axis.

The force acting on a charge placed at the origin is simply Since , the force is directed along the -axis.   Next: Gauss' Law Up: Electricity Previous: Example 3.2: Electrostatic force between
Richard Fitzpatrick 2007-07-14