Forces between charged bodies You should be familiar with the idea of magnets attracting or repelling depending on which combination of poles is used. This is also the case for electrostatic charges. If both are positive or negative they repel If the forces are opposite then the objects are attracted. This fact should be obvious when you consider the formula for the electrostatic force later. Remember forces are vectors!!
Forces between charged bodies + + + + + + + + If we use some sensitive electronic scales we can detect the forces between two identically charged rods. However when this is done in reality the result is not as expected – can you explain why? + + + + + + + + You should pay attention to what happens to the size of the force when the size of charge (rod) changes and as the displacement changes.
Charles Augustin de Coulomb On of them, published in 1785, discussed the inverse square law of forces between two charged particles - as you move charges apart, the force between them decreases 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”. • Hence the unit of electrical charge is named after him. Coulomb was one of the first people to start creating the metric system. • He died in 1806. Charles Augustin de Coulomb • Born in 1736 in Angoulême, France. • Educated at the Ecole du Genie at Mezieres (sort of the French equivalent of universities like Oxford, Harvard, etc.) from which he graduated in 1761. • Served as a military engineer in the West Indies and other French outposts, until 1781 when he was permanently stationed in Paris and devoted more time to scientific research. • Between 1785-91 he published seven memoirs (papers) on physics.
The Torsion Balance When Coulomb was doing his original experiments he decided to use a torsion balance to measure the forces between charges. 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 ensured that the spheres were all the same material, 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 1:1
Inside Coulomb’s torsion balance are two pith balls Inside Coulomb’s torsion balance are two pith balls. One is mounted and unmovable, the other can roll around. When the two pith balls are energized by an electrostatic charge, the moveable one will twist away from the fixed one provided both receive the same type of charge (positive or negative). It will twist towards the stationary pith ball, if they receive different charges. The distance it rolls is used to measure the electrostatic force.
Coulomb was able to measure the torsional force on the fibre with the scale near the top of the device and the distance between the balls on the scale that circumscribed the jar. He derived a mathematical equation that described the relationship between these two variables. The force between two small, charged spheres is shown to be proportional to the magnitude of either charge and inversely proportional to the square of the distance between centres.
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… Coulombs Law F = kQ1Q2 r2 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… F = Gm1m2 r2 r F Q1 Q2
If the objects are in air then the constant can be given a value of 9.0 *109 Nm2C-2 Therefore the correct formula takes this into account since k= 1/4o Where o is the permitivity of free space and so F = 1 Q1Q2 4o r2 However if the charged objects are not in a vacuum or air we have to take into account the medium they are in and therefore the permitivity would change.