5.3 Coulomb's law (Page 12/11)

University physics volume 2 Page 1 / 11

By the end of this section, you will be able to:

Describe the electric force, both qualitatively and quantitatively
Calculate the force that charges exert on each other
Determine the direction of the electric force for different source charges
Correctly describe and apply the superposition principle for multiple source charges

Experiments with electric charges have shown that if two objects each have electric charge, then they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. (Interestingly, the force does not depend on the mass of the objects.) The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.

Let

$q_{1}, q_{2} =$ the net electric charges of the two objects;
${\vec{r}}_{12} =$ the vector displacement from $q_{1}$ to $q_{2}$ .

The electric force $\vec{F}$ on one of the charges is proportional to the magnitude of its own charge and the magnitude of the other charge, and is inversely proportional to the square of the distance between them:

F \propto \frac{q_{1} q_{2}}{r_{12}^{2}} .

This proportionality becomes an equality with the introduction of a proportionality constant. For reasons that will become clear in a later chapter, the proportionality constant that we use is actually a collection of constants. (We discuss this constant shortly.)

Coulomb’s law

The electric force (or Coulomb force ) between two electrically charged particles is equal to

{\vec{F}}_{12} (r) = \frac{1}{4 π ε_{0}} \frac{| q_{1} q_{2} |}{r_{12}^{2}} {\hat{r}}_{12}

We use absolute value signs around the product $q_{1} q_{2}$ because one of the charges may be negative, but the magnitude of the force is always positive. The unit vector $\hat{r}$ points directly from the charge $q_{1}$ toward $q_{2}$ . If $q_{1}$ and $q_{2}$ have the same sign, the force vector on $q_{2}$ points away from $q_{1}$ ; if they have opposite signs, the force on $q_{2}$ points toward $q_{1}$ ( [link] ).

In part a, two charges q one and q two are shown separated by a distance r. Force vector arrow F one two points toward left and acts on q one. Force vector arrow F two one points toward right and acts on q two. Both forces act in opposite directions and are represented by arrows of same length. In part b, two charges q one and q two are shown at a distance r. Force vector arrow F one two points toward right and acts on q one. Force vector arrow F two one points toward left and acts on q two. Both forces act toward each other and are represented by arrows of same length. — The electrostatic force $\vec{F}$ between point charges $q_{1}$ and $q_{2}$ separated by a distance r is given by Coulomb’s law. Note that Newton’s third law (every force exerted creates an equal and opposite force) applies as usual—the force on $q_{1}$ is equal in magnitude and opposite in direction to the force it exerts on $q_{2}$ . (a) Like charges; (b) unlike charges.

It is important to note that the electric force is not constant; it is a function of the separation distance between the two charges. If either the test charge or the source charge (or both) move, then $\vec{r}$ changes, and therefore so does the force. An immediate consequence of this is that direct application of Newton’s laws with this force can be mathematically difficult, depending on the specific problem at hand. It can (usually) be done, but we almost always look for easier methods of calculating whatever physical quantity we are interested in. (Conservation of energy is the most common choice.)

Finally, the new constant $ε_{0}$ in Coulomb’s law is called the permittivity of free space , or (better) the permittivity of vacuum . It has a very important physical meaning that we will discuss in a later chapter; for now, it is simply an empirical proportionality constant. Its numerical value (to three significant figures) turns out to be

<< Chapter < Page Page > Chapter >>

Practice Key Terms 6

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask

©flickr: Francisco	U.S. Civil War Pre-test By Danielle Stephens Start Quiz
	Engineering Communication MCQ By Steve Gibbs Start Quiz
	NCE Ch 07 Lifestyle Career Development By Anh Dao Start Quiz
	Nutrition Exam By Hannah Sheth Start Quiz
	Excel 2007 Quiz By Lakeima Roberts Start Quiz
	10 Biology 10 Cell Reproduction MCQ By OpenStax Start Quiz
	2 AP 02 Chemical Level of Organization MCQ By OpenStax Start Quiz
	19 Biology 19 The Evolution of Populations MCQ By OpenStax Start Quiz
	25 AP 25 Urinary System MCQ By OpenStax Start Quiz
	12 AP Key Terms 12 The Nervous System By OpenStax Start Key Terms