Next: Example 3.2: Electrostatic force between
Up: Electricity
Previous: Worked Examples
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