Four Chapter 3

Electric Forces – Coulomb’s Law

• Charles Coulomb showed that the electrical force between charges is inversely proportional to the square of the distance between the charges, and directly proportional to the product of the charges.

• To do this, he used a torsion balance.

• The forces between charges on the spheres causes the balance to turn.
  • By knowing the torsional properties of the balance, and changing the distance between spheres of constant charge, Coulomb was able to find the relationship between distance between charges and the force exerted between the charges
  • By placing a constant charge on the spheres, and then varying the distance between the spheres, a table of values of angle of turning versus distance can be produced.
  • A graph of this table can be made, and using graphical techniques, an equation for the graph can be determined. Since the amount of turning is proportional to the force between the charges, this equation will verify the inverse relationship between force and distance.
  • Similarly, Coulomb found the relationship between the amount of charge on the spheres and the force.
  • Coulomb places a charge on the sphere on the small stand, touches this sphere to the sphere on one end of the balance. He assumes that the charge on the sphere on the stand is shared equally with the sphere on the end of the balance, and he defines this charge as one unit. The sphere on the stand is then placed a predetermined distance from the charged sphere on the balance. The angle of rotation is measured. Coulomb now removes the charge on the sphere on the stand, and then touches it to the sphere on the balance. Again he assumes equal charge sharing. He now has 0.5 units of charge on each. The sphere on the stand is placed the same distance away from the balance sphere. Rotation is measured. This process is repeated over and over in order to construct a table of rotation versus charge.
  • A graph of this table can be made, and using graphical techniques, an equation for the graph can be determined. Since the amount of turning is proportional to the force between the charges, this equation will verify the direct relationship between the product of the charges.
• Combining the two proportionality equations into one equation gives:

k is Coulombs constant

k = 8.99 X 10⁹Nm²/C²

• Coulomb’s law works for point charges only and therefore real objects must be spaced far apart for the law to apply.
• The unit of charge is defined in terms of the force between two current carrying wires. This is to be explained later in the course.
• The unit of charge is the Coulomb (C)
  • 1 C would be about = the charge passing through a 60 W light bulb in 2 s.
  • 1 lightning strike delivers 1 to 3 C of charge.
• The value of k is determined experimentally by measuring the force and distance between 2 objects with known charge. The information is then substituted into Coulomb’s law and k is solved for.
• Below is a table which compares compares gravitational forces to electrical forces. Below the table is an example showing how Coulomb's law can be used.

December 6, 2013