Evans SPH 4U1

Physics Grade 12

Unit 6: Electricity

Note 3: Coulomb's Law


Reference: Chapter 7.2


We not only need to know whether objects attract or repel but we also would like to know the size of the electric force between them.


Coulomb’s Law

Through experimentation (1785) Charles Coulomb described the quantitative nature of the electric force between charged particles. He used a torsion balance like Cavandish’s in his study of gravitational forces.  The difference was instead of using small masses, Coulomb used electric force between charged spheres to cause the torsion balance to rotate.

·         By varying the distance between the spheres he discovered that:

·         By touching either charged sphere with an identical neutral sphere he was able to divide its charge in half and note the resulting effect of the electric force.  He found:   

·         Combing the two we have Coulomb’s Law:    

where    (determined by using a torsional  balance)


The Unit of Electric Charge – the natural unit is the element charge (e) which is simply the quantity of charge carried by one electron (or proton)


Coulomb’s Law

Coulomb proposed a law that is strikingly similar to Newton’s Law of Universal Gravitation.  Coulomb’s law states that the force of electrostatic attraction or repulsion between 2 small (point) charges or charged bodies is:

·         Directly proportional to the quantity of charge on each body in the pair.

·         Inversely proportional to the square of the distance between the charges.

·         Mathematically,  

where Fe is the force of electrostatic attraction or repulsion,    

d is the distance between charges

qa, qb are the quantity of Net charges on the body





·         Combing we have Coulomb’s Law:    where 

k is the proportionality constant called Coulomb’s constant and it is ONLY for our medium.

·         Only valid for point charges i.e. A & B must be far apart compared to their dimensions.

·         Electric charge is measured in coulombs. One Coulomb is the aggregate charge on a congregation of 6.24 x 1018 electrons.

·         Coulomb’s Law has a vector nature.  A charged particle may be subject to more than one force at a time & the Net Force must be found by adding vectorially.


Text Questions:

Page 331 #'s 1, 5,6,7

Page 334 #'s 9

Page 335 # 4



1.      Two small electrified objects A & B are separated by 0.03 meter, and repel each other with a force of 4.0 x 10 –5 N.  If we move body A an additional 0.03 meter away what is the electric force now? ( Answer: 1.0 x 10-5 N)


2.      Three equally charged objects are located as shown (on blackboard in class) .  The electric force exerted by A on B is 3.0 x 10 –6 N.

a.       What electric force does C exert upon B? (Answer: 1.2 x 10 -5 N [L])

b.      What is the net electric force on B? (Answer: 9.0 x 10 -6 N [L])






3.      Calculate the magnitude of the force between charges of 5.0x 10 –8 C and 1.0 x 10 –7 C if they are 5.0 cm apart. (Answer: 1.8 x 10-2N)


4.      Four identical conducting spheres mounted on Dry Ice pucks are held on a smooth level table at the four corners of a square.  Two of them carry a charge of +q and the other two carry a charge of –q each, as shown in the diagram below.

a.             Make a vector diagram showing the electric forces on sphere 1.

b.            If all the pucks are released at the same time, in what direction will each of them move? ( Answer: To the centre)







5.      Suppose that we place 3 small charged spheres, with equal charges on them, as shown  (on blackboard in class).  Sphere C exerts a force of 4.0x 10 –6 N on B.

a.       What force does A exert on B? (Answer: 3.0 x 10 -6N [away])

b.      What is the net force on B? (Answer: 5.0N[S53 degreesW])







6.     Two bodies are placed X apart.  Both carry net positive charges.  Determine the effect on the magnitude of the electrostatic force of repulsion if :

a.       The distance is changed to 2 X  (answer: divided by 4)

b.      The quantity of charge on one object is tripled  (answer: x 3)

c.       The quantity of charge on the 2nd object is quadrupled ( answer: x4)

d.      All of the above charges are made simultaneously (answer: x 3)


7.      Triangle ABC is a right-angled isosceles triangle (see diagram on blackboard in class).  Point charges of equal magnitude (1.0 mC) are placed at the vertices.  Determine the magnitude and direction of the Net electric force on C by A & B. 

       (Answer: 1.3N [W15 degreesS])