Electric Fields

Coulomb's Law

Remember, UNLIKE charges attract,

or

and LIKE charges repel,

or

What determines the magnitude of this electric force F?

The force F is directly proportional to the charges Q and q,F Q q

The force F is inversely proportional to thesquareof the distance r between the charges,

F 1 / r^{2}

^{}

F 1 / r^{2}

^{}

F 1 / r^{2}

We can combine these asF Q q / r^{2}

Whileproportionalitiesare good for qualitative discussions and comparisons,equationsare much easier to use for calculations. We can change this to anequationwith aconstant of proportionality, k.F = k Q q / r^{2}

This constant of proportionality, k, depends upon the units we use. If we measure force F in newtons (N), distance r in meters (m), and charges Q and q in coulombs (C), then k has a value ofk = 9 x 10^{9}N m^{2}/C^{2}

Now we must ask, just what is a coulomb of charge, anyway?

The electric charge of an electron or a proton is labeled e and is equal to . . .

Coulomb's Law describes the force F between two electric charges, Q and q, a distance r apart,

What is the force between two positive charges, 1 C and 2 C, when they are separated by a distance of 1 m?

Remember,

force is a vector. Coulomb's Law lets us calculate themagnitudeof the electric force but we must still keep in mind thatforce is a vector!Example of Coulomb's LawWe will also sometime write this "Coulomb's constant" as

where "epsilon-zero" is

and is known as the "permitivity of free space". That

namesounds more ominous than it needs to. It is simply another form of "Coulomb's constant" -- and nothing more! There are major situations or major equations where we end up with a factor ofwhich is then more convenient to write as

You may have looked at the Cavendish Balance when you talked about Gravity. Cavendish used averydelicate balance to measure incredibly small forces. Coulomb, in measuring the electrical forces, had larger forces to work with. Here is a sketch of the balance he used to measure electrical forces and determine the one over r-squared characteristic of the electrical force:

(c) Doug Davis, 2002; all rights reserved

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