Brooklyn College 1

Coulomb’s Law

Purpose

1. To be introduced to Coulomb’s law.

2. To study the dependence of the Coulomb’s force on the values of point charges and the dependence of the Coulomb

force on the separation distance between the point charges.

Introduction

You may have noticed some sparks while taking off your wool sweeter. Why does this happen?

An atom is a nucleus that has particles called protons and neutrons. The nucleus is surrounded by electrons of number

equal to the number of protons in the nucleus. The protons are said to have positive charge and the electrons are said to

have negative charge, and since their number is equal, so the atom as a whole has no net electric charge, it is neutral.

If a plastic rod is rubbed with a piece of fur, the electrons in the atoms of the fur gain energy and transfer to the plastic

rod. Remember that atoms are neutral, so the extra electrons transferred to the plastic rod cause it to become

negatively charged. If we do the same to another plastic rod and bring the two rods close to each other they repel each

other. Therefore, we conclude that negative charges repel each other.

If a glass rod is rubbed by a piece of silk, the electrons in the atoms of the glass acquire energy and transfer to the silk, so

the atoms of the glass rod now has fewer electrons than the protons in the nucleus, so the glass rod is now positively

charged. If we do the same to another glass rod and bring the two rods close to each other, they repel each other. So we

conclude that positive charges also repel each other. So like charges repel each other.

Now what happens if we bring a rubbed plastic rod close to a rubbed glass rod? They attract. Therefore unlike charges

attract each other.

Coulomb was able to quantify the force between two point (concentrated at a point) charges that are static (stationary)

charges. The unit of the charge is the Coulomb, ‘ ’ in honor of the scientist Coulomb. He found that the magnitude of

the force, called the electrostatic or Coulomb force, is proportional to the product of the absolute value of the charges:

Now is the separation between the charges, r is increased, we should expect the force of each of them on the other

should decrease. Coulomb found that the electrostatic Coulomb force is inversely proportional to the square of the

separation, r between the two point charges.

From Coulomb’s law the magnitude of the electrostatic Coulomb force between

two point charges, and separated by a distance, is

where is a constant called Coulomb constant, .

The direction of the force, can be determined by applying the rule that like charges repel each other and unlike

charges attract each other.

Figure 1: two point charges

separated by a distance .

Brooklyn College 2

Running the experiment (The data sheet is on page 3)

Part 1: Dependence of the Coulomb electrostatic force on the separation between the charges

1) Consider figure (1). Assume we have two point charges. The first has a charge and the second has a

charge . If the distance between the two charges, , calculate the electrostatic force according to

Coulomb’s law between the charges. In which direction is the force of on ?

2) Open the simulator http://ophysics.com/em1.html

Notice the values of the two charges and the separation r between them. Compare the magnitude of the force displayed

by the simulator to your calculated value in step 1. Also check the direction of the forces.

3) Keep the values of the charges the same as in step 1 and calculate the electrostatic Coulomb’s force for the

separations: Record in table 1. Record also from step (1) for

4) Now using the simulator, click and drag the charge B, ( ) to the separations of step 3, and each time compare the

Coulomb’s force as given by the simulator to your calculated values of step 3. Record in table 1.

5) Plot a graph of the magnitude of the electrostatic force, versus . Should the graph be a straight line? Should

it pass through the origin?

6) Plot a graph of the versus . Should the graph be a straight line? What should the value of the slope be?

Calculate the slope of the graph and compare to your prediction of the value of the slope.

Part 2: Dependence of the Coulomb electrostatic force on the value of the charges

1) If the charges of part 1 are at a separation , calculate the magnitude of the force. In

what direction is the force of charge B, ( ) on charge A, ( )?

2) Now in the simulator, click and drag charge B, ( ) so that . Record the value of the magnitude of the force

displayed by the simulator.

3) Keeping the separation, , change the value of each of the two charges, and , so that equal to

then then then . Each time record in table 2 the value of the magnitude

of the force, as measured by the simulator. Record also the value from step (1) in table 2.

4) Plot a graph of the magnitude of the force, versus . Calculate the slope. How does the slope relate to the

values of and ?

5) Assume , and ,

a) What do you expect the magnitude and direction of the force of on to be if their separation is ?

b) For the same separation, what do you expect the magnitude and direction of the force of on to be?

c) Now try it using the simulator. Is the result, using the simulator, the same as your expectation?

d) Do you understand now the concept of ‘mutual force’? Does Coulomb’s force demonstrate Newton’s 3rd law?

Brooklyn College 3

Data sheet Name: Group: Date experiment performed:

Part 1: Dependence of the Coulomb electrostatic force on the separation between the charges

Step 1) , Calculation of : Direction of of on :

Step 2) measured by the simulator:

Steps (3) to (6):

Table 1

( ) Calculated measured by simulator

10

8

6

4

2

Show your calculations here:

Step 5) Is the graph a straight line? Should it pass through the origin?

Step 6) Should the graph be a straight line? What should the value of the slope be?

Calculation of the slope: Was your expectation correct?

Part 2: Dependence of the Coulomb electrostatic force on the value of the charges

Step 1) , Calculation of : Direction of of on :

Step 2) measured by the simulator:

Step 3)

Table 2

( ) ( ) ( ) measured by simulator

Step 4) Calculation of slope of graph of versus :

How does the slope relate to the values of and ?

Step 5) Answers to: a)

b)

c)

d)