## Charge in an Electric Field

Faraday refined this idea of an actual electric force field.  You probably were first exposed to the idea of fields in elementary school when you examined magnetic field lines using iron filings (we will do this later in the semester).  Faraday discusses gravitational, electric, and magnetic force fields.

The idea of a force field is used to explain the “action at a distance” which is a common characteristic of the electric, magnetic, and gravitational forces. You can think of a gravitational field as an imaginary spiderweb emanating out from mass going all the way to infinity.  Likewise with an electric field for charge.  There is actually a lot more truth to this spiderweb than meets the idea, but we can save a discussion of virtual gravitons and photons for another day.

If we place a charge in this spiderweb, the charge will interact with the web.  We can actually draw arrows on the field lines to depict the direction of the force.  With a gravitational field, there is no ambiguity as gravity is always attractive.  With the electric force, we have a choice of the polarity of charge.  By convention, fields are drawn assuming a positive test charge.

Your text defines E as the Electric Field Strength.  I prefer to call it the Electric Force Field Strength, but that is a mouthful.  If we put a charge q, in an field of an Electric Force Field Strength E, then the magnitude of the force is given by

F = qE

Note, that both Force and Field Strength are vectors.

The most common units for Electric Field Strength are Newtons/Coulomb or N/C.  However, at times, you will also see the equivalent  unit Volt/meter which will be discussed later.

One way to consider this is to think about gravitation, where you are dealing with the gravitational force and mass, with

F = mg

In this case  E = F/q   and g = F/m are similar principles.  The main difference is that inertia also has a relation to mass.

When doing problems with this equation we often assume the Electric Field is uniform or the same everywhere.  For instance, near the surface of the Earth, we assume the gravitational field strength is the same everywhere, or a constant g downwards. We know in reality that the Earth is not flat, and thus this is only an approximation.

Likewise, between two oppositely charged parallel plates, the electric field is generally uniform, pointing from the positive plate to the negative plate.  Again, this is a good approximation near the center of two large plates, but this assumption breaks down near the edges.

The other things to consider here is that a charge in a field is being accelerated.  The electric field can actually do work and give a charge energy!