Electric Fields

[PHYSICS TUTORIAL]

This section discusses the important concept of an electric field. Fields and field lines will be explained, and several important formulas will be given.

You may have noticed that certain forces can act on objects even when they are not touching. Take gravity for instance. The Earth and the moon do not touch each other (thank goodness!) but the force of gravity keeps the moon in orbit. The electrostatic force acts in this way also. The are around any charged object is known as that object's electric field.

We can quantitatively determine the strength of a electric field. We begin by imagining a large charged object. Now bring an object with a charge of the same polarity, but smaller magnitude, close to the first charge. The strength of the electric field at the location of the particle is the force that is acting on the second charge divided by that charge. So if we have a third charge, identical to the second, and we bring it closer to the large object, then the force on that particle will be greater, and we know that the electric field in that region is greater. We represent this with the equations:
[E=|F|/|q|]
E is in newtons per coulomb, F is in newtons, q is in coulombs.
We can also substitute Coulomb's Law into this equation to obtain:
[E=k|q|/r^2]
E = k (a special constant) * charge / the square of the distance between the charges
k = 8.9875*109 N*M2/C2

The principle of superposition holds for electric fields. The electric field of a group of charges is equal to the vector sum of their electric fields.

We often want to visualize the shape of an electric field. To do this, we use electric field lines. These lines tell us two things about the electric field:

  1. The electric field vector, E, is tangent to the lines at every point
  2. The density of the lines through a unit of area on a surface perpendicular to them is proportional to the strength of the electric field for that region
Look at the picture below. Note that the direction of the arrows and the sign of the charge. Lets pretend that these charges do not affect one another. The electric field lines shown result. For these arrows, we say the test charge is positive. By convention, the test charge is always positive. A positive charge placed near the shown charges would be pushed in the direction of the arrows.
[FIELD LINES]
We follow three basic rules when we draw field lines for a group of charges:
  1. The lines must begin on positive charges or infinity, and must end on negative charges or infinity
  2. The number of lines leaving a positive charge and the number of lines approaching a negative charge indicate the magnitude of the charge
  3. Lines may NOT cross
If we had two charges of equal magnitude but opposite charge, then the electric field line diagram would look something like the picture below.
[FIELD LINES]

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