Note-A-Rific: Coulomb

Charles Augustin de Coulomb

Before getting into all the hard core physics that surrounds him, it’s a good idea to understand a little about Coulomb.

  • He was born in 1736 in Angoulęme, France.
  • He received the majority of his higher education at the Ecole du Genie at Mezieres (sort of the French equivalent of universities like Oxford, Harvard, etc.) from which he graduated in 1761.
  • He then spent some time serving as a military engineer in the West Indies and other French outposts, until 1781 when he was permanently stationed in Paris and was able to devote more time to scientific research.
  • Between 1785-91 he published seven memoirs (papers) on physics.
    • On of them, published in 1785, discussed the inverse square law of forces between two charged particles. This just means that as you move charges apart, the force between them starts to decrease faster and faster (exponentially).
    • In a later memoir he showed that the force is also proportional to the product of the charges -a relationship now called “Coulomb’s Law”.
  • For his work the unit of electrical charge is named after him. This is interesting in that Coulomb was one of the first people to start creating the metric system.
  • He died in 1806.

The Torsion Balance

When Coulomb was doing his original experiments he decided to use a torsion balance to measure the forces between charges.

  • You already learned about a torsion balance in Physics 20 when you discussed Henry Cavendish’s experiment to measure the value of “G” , the universal gravitational constant.  Review Cavendish’s work (page 223 in your text).
  • Coulomb was actually doing his experiments about 10 years before Cavendish.
  • He set up his apparatus as shown below with all spheres charged the same way…

 

 

 

 

 

 

 

 

 

 

 

 


  • Because like charges repel, the spheres on the torsion balance twist away from the other balls.
  • By knowing the distance between the balls, the force needed to twist them, and the charges on the balls, he could figure out a formula.

 

The problem is, how could Coulomb know how much charge was on the spheres.

  • They had electroscopes, but all you can really do with those is tell if there is a charge, not how much.
  • His solution was to charge the spheres by conduction.
    • He made sure that all his spheres were made of the same material, and were the same size and shape.
    • He would then build up a charge on one (usually by friction) and touch it to one other sphere.
    • Since they are the same size, shape, material, the charge is shared evenly between the two, so at least Coulomb knows the ratio of their charges is one-to-one.

 

 

 

 

 

 

 

 


After all this work Coulomb finally came with a formula that could be used to calculate the force between any two charges separated by a distance…

F = force in Newtons

q = charge in Coulombs

r = distance between the charges in metres

k = 8.99 x 109 Nm2/C2

Notice that this formula looks almost identical to the formula for Universal Gravitation…

 

Example: One charge of 1.0 C is 1.5m away from a –1.0 C charge. What is the force they exert on each other?

 

 

The negative sign just means that one charge is positive, the other is negative, so they are pulling together.

 

Wow, that’s a lot of force!

  • It is VERY rare to find charges as big as this.
  • In the lab or in everyday life charges are usually in the range of about 10 -6C (1mC).

Multiple Charges in One Dimension (Linear)

Things get a bit more interesting when you start to consider questions that have more than two charges.

  • Almost always you will deal with at most three charges in these linear problems.
  • In the following example you have three charges lined up and are asked to calculate the net force acting on one of them…

 

Example: The following three charges are arranged as shown. Calculate the net force acting on the charge on the far right (charge #3).

 

 

 

 

 


To solve a problem like this you have to do it in steps. Calculate the force between one pair of charges, then the next pair of charges, and so on until you have figured all the forces. Let’s look at the steps for this problem:

    1. Calculate the force that charge 1 exerts on charge 3

It does NOT matter that there is another charge in between these two… ignore it! It will not effect the calculations that we are doing for these two.

Notice that the total distance between charge #1 and #2 is 3.1 m , since we needed to add 1.4 m and 1.7 m .

The negative sign just tells us the charges are opposite, so the force is attractive. Charge #1 is pulling charge #3 to the left, and vice versa.

 

    1. Calculate the force that charge 2 exerts on charge 3

Same thing, only now we are dealing with two negative charges, so the force will be repulsive.

The positive sign tells you that the charges are either both negative or both positive, so the force is repulsive. Charge #2 is pushing #3 to the right.

 

    1. Add you values to find the net force.

We now need to add the two values from above, being careful about directions.

We had a 4.9 x 10-2N force pushing the charge to the left, which just happens to be the direction we usually call negative, so we’ll leave the negative sign on it. We also have a 2.5 x 10-1N force pushing to the right. Again, we just happen to be lucky that the sign on the force (positive) agrees with the fact that we usually say right is positive.

- 4.9 x 10-2N + 2.5 x 10-1N = 2.0 x 10-1N

So, that is the net force acting on the 3rd charge.

Multiple Charges in 2 Dimensions

Doing questions with charges in multiple dimensions are the same as the question you did above. You just need to be careful about directions and use vectors to figure out the problem.

  • Look at the example problem #2 that is on page 590 – 592.
  • Understand the method used to solve this type of problem.