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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