23.8 - Describing the force exerted by an external electric field
In this section, we shift our attention from the field
caused by a charge to the force exerted on a charge
by an external electric field. Such a field could be
created by just one other charged particle, or it could
be created by a much larger number of charged
particles.
Fields are used in many everyday devices. For
example, a field is used in some high-end inkjet
printers to control the direction of charged ink droplets
as they fly toward a sheet of paper. A charged
camera flash can store energy in a field created by
more than a trillion excess electrons. Given this huge
number, determining the overall field by summing the
individual fields created by each electron would be a bit tedious. Instead, placing a test
charge in the field and observing the force that the field exerts on it can determine the
nature of the field.
When a charged particle is in an electric field, the equation in Equation 1 can be used to
describe the amount of force that the field exerts on the particle. This equation comes
from the defining equation for the electric field, solved for the force.
A point charge creates a field that diminishes with the distance from the charge. This
means the force it exerts on a test charge will vary by location. However, engineers are
clever enough to create nearly uniform fields, fields whose strength and direction is the
same at all locations within the field. For instance, there is a nearly uniform field in the
center of the region between two large, oppositely charged flat plates separated by a
small distance. In Example 1, you are asked to determine the force exerted on an
electron by such a field.
Newton’s second law enables you to determine the acceleration of the electron in this
electric field and we do so in Example 2. The force exerted by the field is divided by the
mass of an electron to determine the acceleration. The result is a large acceleration,
having a magnitude of approximately 350,000 m/s^2.
This acceleration is caused by a relatively weak field (it is well below the maximum
allowed for human exposure by government safety standards). At the acceleration
stated, the speed of the electron would quickly approach that of light, and the
acceleration would have to diminish due to the relativistic effects predicted by Albert
Einstein.
Polluting smokestacks. Electrostatic precipitators could electrically charge this
particulate matter and use electric fields to remove it from the effluent.