Welcome to the Field

Like the gravitational force, the electrical force acts over a distance when two objects are not touching. A helpful way to describe this type of interaction is with the concept of the field, developed by the British scientist Michael Faraday (1791 - 1867).

According to Faraday, an electric field extends outward from every charge and permeates all space. If a second charge is placed near the first charge, there is in interaction between this charge and the electrical field of the first, producing a force.

The nature of an electric field (its strength and position in space) can be investigated with a small positive test charge. By a test charge we mean a charge so small that its field does not significantly alter the field being tested.

The force of a tiny positive test charge q placed at various locations near a single positive charge Q is shown in the figure. Agreeing with Coulomb’s Law, the further away the charge then the smaller the force. In each case the force is directed radially outward from Q. The strength of the electric field at any point in space, E, is defined in terms of the force on the test charge at that point.

Definition of Electric Field

• The electric field, E, represents a region in space outside an electric charge. If another electric charge enters this field, then equal and opposite forces acting on each charge will be created.
• Electric field strength, E, is a vector and has units of N/C.

Field Strength and Coulomb's Law

The formula for electric field strength can be rewritten to solve for force, F.

(Note that this formula is the electrical equivalent to Newton’s 2nd law for the force on a mass in a gravitational field:

In electricity, charge, q, plays the role of mass, m, and electric field, E, plays the role of gravitational field, g.

A second equation for electric field strength can be derived using the two equations that we now have for electric force.

Visualizing the Electric Field

The electric field can be visualized with electric field lines. The properties of field lines are summarized as follows:

1. The field lines indicate the direction of the electric field (they always point in the direction of the force acting on a positive test charge); the force points in the direction tangent to the field line at any point.
2. The lines are drawn so that the magnitude of the electric field is proportional to the number of lines per unit area. The closer the lines are to each other, the stronger the field.
3. Electric field lines start on positive charges and end on negative charges, and the number starting or ending is proportional to the magnitude of the charge.

field lines around a positive charge Q

field lines around a negative charge Q

field lines around equal but opposite charges

field lines around equal positive charges

field lines around unequal and opposite charges

field lines between parallel oppositely charged plates

Electric Fields and Conductors

Consider the sphere of a Van de Graff generator. Is there an electric field within the metal of the sphere?

The electric field inside a conductor is zero in the static situation that is, when the charges are at rest. If there were an electric field within a condctor, there would be a force on the free electrons. The electrons would move until they reached positions where the electric field, and therefore the electric force on them , did become zero.

There are two consequences of this:

1. Any net charge on a conductor distributes itself on the surface of the conductor.
2. The electric field is always perpendicular to the surface outside of a conductor.

 

Examples

5. Determine the electric field strength 0.10m from a point charge Q which carries a charge of 0.20µC. Then use this electric field strength E to determine the force on a second point charge, q, with a charge of 0.80µC at a distance of 0.10m from Q.
6. A particle of mass 0.0010kg has an excess charge of +1.0μC. The particle is located in a region between two oppositely charged parallel plates where the electric field is uniform and has a magnitude of 1000N/C. Determine . . .
   1. The magnitude of the force acting on the particle
   2. Rate of acceleration of the particle
   3. If the distance between the plates is 0.010m and the particle is initially at rest at a point close to the positive plate, determine the velocity of the particle just before it strikes the negative plate.
      
7. A proton traveling at 3.0×10⁶m/s enters a region where the electric field has a magnitude of 3.0×10⁵N/C. The electric field is uniform and retards the proton’s motion. Determine
   1. the distance the proton will travel before coming to a momentary halt
   2. the time required for the proton to travel this distance.
      
8. Two point charges, Q₁=+5.0μC and Q₂=-5.0μC, are located on the y-axis at y=+3.0m and on the y-axis at y=-3.0m respectively. Determine the magnitude and direction of the electric field on the x-axis at x=+4.0m.

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