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*Question:* A particle of charge
is located
on the -axis at coordinate
. A second particle of
charge
is placed on the -axis at
. What is
the magnitude and direction of the total electrostatic force acting on a third particle
of charge
placed at the origin ()?

*Solution:* The force acting between charges 1 and 3 is
given by

Since , the force is repulsive. This means that the force exerted by charge
1 on charge 3 is directed along the -axis
(*i.e.*, from charge 1 towards charge 3), and is of magnitude . Thus,
. Here, we adopt the convention that forces directed
along the -axis are positive, and *vice versa*. The force acting between charges 2 and 3
is given by

Since , the force is attractive. This means that the force exerted
by charge 2 on charge 3 is directed along the -axis (*i.e.*, from
charge 3 towards charge 2), and is of magnitude . Thus,
.
The resultant force acting on charge 3 is the
algebraic sum of the forces exerted by charges 1 and 2 separately (the sum is algebraic
because all the
forces act along the -axis). It follows that

Thus, the magnitude of the total force acting on charge 3 is
, and the force is directed along the -axis (since ).

** Next:** Example 3.2: Electrostatic force between
** Up:** Electricity
** Previous:** Worked Examples
Richard Fitzpatrick
2007-07-14