Electric Charges 03 - Electric Fields

OPENING QUESTIONS: What are the SI Units for an electrical field? What do those units tell us about the nature of an electric field?

OBJECTIVE:  I will be able to sketch the electrical field lines between two point charges (either positive or negative) after today's class



  • Test Charge: A mathematical construct-- a charge that does not exert any influence on surrounding particles but IS influenced by other electric fields.
  • Conductors - materials where electrons can roam
  • Insulators - materials that keep their electrons close to home
  • coulomb - a unit of electrical charge (see below)


  • e-mass = 9.1 x 10-31 kg
  • charge of an electron = 1.60 x 10-19 coulombs (C)
  • ke = 8.987 x 109 Nm2/C2


      1. Electrical Force: Fe = (keq1q2)/r2
      • Electrical Field: E = Fe / qo where qo  = a positive test charge
      1. #1 and #2 (above) work well together to tell us about the strength of the electrical field at some distance (r) away from a point source:

        E = (keq)/r2

        Please keep in mind that E is a vector and that we will frequently need to componantize 'r' in terms of unit vectors i and j


Let's get our homework on the board -- be prepared to answer questions about the problem:

4, 10, 15 first

26, 33 next


Let's take a gander at the opening question

Our most-gracious-and-humble author kind of glosses over his discussion of field lines... for a somewhat more comprehensive discussion please take a look at THIS (from the physicsclassroom.com)


ACK! A problem with the "Pitfall Prevention 23.2" on page 709.

A VERY helpful way to help us understand the nature of electrical field lines is for us to 'place' a test charge between two objects with electrical charge. In that thought experiment, the test charge "follows" the field lines between those two objects.

As you might expect the test charge (since it is positive) will move towards the negatively charged object along those field lines and away from a positively charged article-- once again following the path outlined by the electrical field lines.

HOWEVER, what that Pitfall Prevention is trying to tell us is that in the REAL WORLD, objects rarely follow such proscribed paths...

Consider again a comet moving through the solar system. We can very adequately predict the general motion of the comet by sketching gravitational field lines emanating from the sun.

In such a situation, the comet follows a proscribed parabolic orbit described by those field lines.... However, in the 'real' world, that comet experiences perturbations in its orbit as it moves closer to the planets. The closer it gets to the larger planets, the more its orbit is disturbed.

The Rules for drawing electrical field lines:

  1. Draw electrical field strength so that the field leaves a positively charged object and arrives at a negatively charged object
  2. Draw more lines in areas where the field strength is largest-- the density of the field lines indicates larger charge. More lines per area = larger field strength, fewer field lines = smaller field strength
  3. Electrical field lines are ALWAYS drawn perpendicular to the surface of the objects in question
  4. Electric field lines NEVER cross-- As tempting as it might be, each region of space has electric lines unique to that space.

With that in mind: work with your groups to sketch the field lines between the following situations:

1) two point charges with +q and -q charges a distance 'r' apart

2) two point charges with +q and +q a distance of 'r' apart

3) two point charges with +2q and -q a distance of 'r' apart

4) two point charges with -q and - q a distance of 'r' apart


HOMEWORK: Sketch 1, 2, 3 & 4 above

Conceptual Problems C23.1 and C23.4