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## Example 3.2: Electrostatic force between three non-colinear point charges

Question: Suppose that three point charges, , , and , are arranged at the vertices of a right-angled triangle, as shown in the diagram. What is the magnitude and direction of the electrostatic force acting on the third charge if , , , m, and m?

Solution: The magnitude of the force exerted by charge on charge is given by

where use has been made of the Pythagorean theorem. The force is attractive (since charges and are of opposite sign). Hence, the force is directed from charge towards charge , as shown in the diagram. The magnitude of the force exerted by charge on charge is given by

The force is repulsive (since charges and are of the same sign). Hence, the force is directed from charge towards charge , as shown in the diagram. Now, the net force acting on charge is the sum of and . Unfortunately, since and are vectors pointing in different directions, they cannot be added together algebraically. Fortunately, however, their components along the - and -axes can be added algebraically. Now, it is clear, from the diagram, that is directed along the -axis. If follows that

It is also clear, from the diagram, that subtends an angle

with the -axis, and an angle with the -axis. It follows from the conventional laws of vector projection that

The - and -components of the resultant force acting on charge are given by

Thus, from the Pythagorean theorem, the magnitude of the resultant force is

Furthermore, the resultant force subtends an angle

with the -axis, and an angle with the -axis.

Next: Example 3.3: Electric field Up: Electricity Previous: Example 3.1: Electrostatic force between
Richard Fitzpatrick 2007-07-14