13.3. The Coulomb Force Law http://www.ck12.org
The electric field is a vector quantity, and points in the direction that a force felt by a positive charge at that point
would. If we are given the electric field at some point, it is just a matter of multiplication — as illustrated above —
to find the force any chargeq 0 would feel at that point:
F~e
︸︷︷︸
Force on chargeq 0= E~f
︸︷︷︸
Field×︸︷︷︸q 0
ChargeForce on chargeq 0 in an electric fieldNote that this is true forallelectric fields, not just those from point charges. In general, theelectric fieldat a point
is the force apositive test charge of magnitude 1would feel at that point. Any other charge will feel a force along
the same line (but possibly in the other direction) in proportion to its magnitude. In other words, the electric field
can be though of as "force per unit charge".
In the case given above, the field was due to a single charge. Such a field is shown in the figure below. Notice that
this a field due to a positive charge, since the field arrows are pointing outward. The field produced by a point charge
will be radially symmetric i.e., the strength of the field only depends on the distance,r, from the charge, not the
direction; the lengths of the arrows represent the strength of the field.
Example 2
Question: Calculate the electric field a distance of 4.0mm away from a− 2. 0 μC charge. Then, calculate the force
on a− 8. 0 μC charge placed at this point.
Answer: To calculate the electric field we will use the equation
E=
kq
r^2