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Introduction to the Electric Field

Consider a source charge Q and a so-called positive test charge q0.

Source charge Q and three test charges q0
At every point in space, q0 will experience a force from its interaction with charge Q. Since there is a force acting on the charge q0 when present, there should still be "something" there when the test charge q0 is removed. That something is called the electric field, represented by the bold-faced letter E.

The field approach may be summarized as follows:

  1. Charge Q sets up an electric field in space around it.
  2. The resulting field exerts a force on q0 which depends only on the position and magnitude of q0.
The field plays an intermediate role.

field mediation of charge interaction

This approach separates the situation into two parts:

  1. Calculate the electric field created by given charge distribution (will investigate this topic in about two weeks).
  2. Calculate the force exerted on charge placed in field (simple, do today!)
Note that there is a constraint: Introducing q0 must NOT change the positions of the charges responsible for the fields.

Unfortunately the field concept is not yet in its full glory in electrostatics, where all charge distributions are at rest. When charges are moving however, fields are time-dependent (especially if the charges are accelerating, with resulting electromagnetic radiation). The field concept beats out direct charge-charge interactions and the so-called action-at-a-distance approach.

If charge Q moves, how does force at q0 adjust?

Field approach: Field disturbance emanates from Q and propagates to q0 at the speed of light (photons). We will see this from Maxwell's equations late in the semester.
Action-at-a-Distance: Q's acceleration needs to be "felt" instaneously? Hard to reconcile...

Definition of Electric Field:

Definition of Electric Field

Observations:
  1. Dimensions are force per charge, so units are N/C. Later I will tend to use units V/m, after the unit of volts is introduced.
  2. The bold-faced quantities above indicate vectors. The electric field is a vector field, since force is a vector quantity. You already know numerous scalar fields, quantities which vary over space; some examples are temperature and pressure. Vector fields are an extension of the field concept to vector quantities.
  3. The effect of introducing the positive test charge q0 must be minimized, therefore the limiting case is considered.
    4. Superposition of forces (from PHYS207) leads to superposition of the electric field contributions of a group of point charges. (See continued discussion on superposition.)

Electric field for a point charge:

[E for a point charge]

Graphical Representation of the Electric Field:

COMPUTER DEMONSTRATION: The computer program EM Field from Academic Physics Software will permit us to examine the electric fields that result from groups of point charges. First consider a single point charge of +4 units to get a feel for the program, examining in turn field vectors, field directions, and then field lines. Then we proceed to the study of pairs of point charges; first -4 and +4 units (forming a dipole), and then +4 and +4 units.

Also we examine some tranparencies of charge distributions where 8 lines emanate per unit of charge. Paper masks are used to focus our attention near to and far away from the charge distributions.

  1. Single point charge: +4.5
  2. Two identical charges: +3 / +3
  3. Two different unlike charges: +2 / -1
  4. Dipole: -3 / +3

Electric field lines (also known as lines of force) are constructed with the following rules:

  1. The tangent to the field line at any point gives the direction of the electric field there.
  2. Lines of force are drawn to that the "number of lines/unit area" is proportional to the magnitude of the electric field. If close together, the field is strong there, weaker where further apart.
The following observations can be made about field lines:
  1. Field lines never close on themselves or intersect, since the electric field has a unique direction at each point.
  2. Every line connects a positive charge with a negative charge. It may be necessary to imagine charge at infinity for "neutrality". A positive charge serves as a source of lines, a negative charges as a sink.
  3. Field lines behave as if there is a tendency for lines to repel one another. [Examine +Q/-Q and +Q/+Q pairs.]
  4. Close enough to a point charge, the field lines resemble those of an isolated charge.
  5. Far enough away from a group of point charges, there is insignificant difference from a single charge of same magnitude as net charge. [Look at +2Q/-Q pair.]

Concept Check

An Example -- Quiz 1, Fall'97

The Uniform Electric Field

An important field for our consideration is the uniform electric field, a field that has the same magnitude and direction at all points. We will see in a few weeks that an infinite sheet of charge will be used to create the uniform E. This may be realized to a good approximation in the lab by hooking a battery to two isolated parallel metal plates so that they become oppositely charged.

uniform electric field

An electron injected into the region between the plates will experience a force given by F = -e E. The resulting acceleration can be found from Newton's second law. In the region between the plates, the electron will experience a constant acceleration and the resulting parabolic trajectory.

The control of electrons by so-called deflection plates is the principle behind the operation of the cathode-ray tube used in oscilloscopes and many televisions and computer monitors.

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Last updated March 4, 1998.
Copyright George Watson, Univ. of Delaware, 1997.