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## 22 February 2009

### Electric fields and potentials of point charges

The electric FIELD produced by a point charge is E = kQ/d2. The electric POTENTIAL produced by a point charge is V = kQ/d.

Electric field is a vector. This means that the equation E = kQ/d2 gives just the magnitude of the electric field, and therefore the sign if the charge producing the field should NOT be plugged into the equation. The direction of the field is away from a positive charge, and toward a negative charge.

Electric potential is a scalar. This means that the sign of the charge producing the potential SHOULD be plugged into the equation V = kQ/d. Positive charges produce positive potentials; negative charges produce negative potentials.

When more than one charge produces an electric field, the net field is found by vector addition. When more than one charge produces an electric potential, the net potential is found by algebraic addition and subtraction.

I can’t begin to tell you how frustrating it is to go over the above paragraphs 30 times in 15 different ways with 80 different examples… and then to see someone tell me that the electric field due to a couple of charges is “(2-Q)/d.” Aargh!!!

Such is the nature of electricity, though. I have to remind myself time and again how abstract the idea of a “field” is to begin with, let alone potential, the concept of “charge,” the creation of a field or potential… double Aargh!

The only success I’ve found at the physics B level with these topics is through repetition. There is no choice but to ask students quiz questions 30 times in 15 different ways with 80 different examples. If that doesn’t work, give it a rest for a week… then ask a 31st time.

Below are four questions from a fundamentals quiz which get to the heart of electric fields and potentials due to point charges. Can you answer them correctly? (Post a comment with your answer! If you’re wrong, that’s okay… someone will correct you.)

1. What is the electric potential produced by a -3Q charge a distance of 2a away from the charge?

2. What is the magnitude of the electric field produced by a -3Q charge a distance of 2a away from the
charge?

3. In the diagram to the right, what is the magnitude of the electric field produced by the two charges at point P?

4. In the diagram to the right, what is the vertical component of the electric field produced by the –Q charge at point P?

GCJ

(Photo at the top from alexhulbert.com . )