Physics Notes 7.2(Electric Forces:Coulomb's law)

Where Fe is the magnitude of the electric force and r is the distance between the centres of the charged spheres.
Fe (Inversely proportional to) to the square of r
He devised a torsion balance
Coulomb’s experiment
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Coulomb’s apparatus consisted of a silver wire attached to the middle of a light horizontal insulating rod.
AT ONE END of the rod is a pith ball covered in gold foil.
AT THE OTHER END is a paper disk attached to balance the rod.
Coulomb’s apparatus
Coulomb brought an identical stationary ball into contact with the suspended ball.
He charged both balls equally by touching one of them with a charged object.
The two balls then repelled each other, twisting the wire holding the rod until coming to rest some distance away.
Description of Coulomb’s experiment
Fe (is inversely proportional to) the square of r
where r is the distance between the centres of charged spheres
Fe is the magnitude of electric force.
conclusion # 1
Discovered the relationship between the between the magnitude of the electric force and and the charge on 2 spheres.
“By touching either charged sphere with an identical neutral sphere, he was able to divide it’s charge by half.”
conclusions # 2
1) By repeatedly touching a charged sphere with an identical neutral sphere, he was able to reduce the charge to a quarter, and eighth and sixteenth…. of it’s original value.
2)Having the charge on one sphere decreased the force of electrostatic repulsion to half it’s original value, where as having both charged reduce the force to a quarter of it’s original value.
Reasons why it was able to divide in half
Where q1 and q2 are the respective magnitudes of the charges on the two spheres.
conclusion # 2; Fe is directly proportional to q1q2
We create coulomb’s law of electric force:
Fe (directly proportional to) (q1q2)/r^2
Fe = (k*q2*q2)/r^2, where k is a proportionality constant, knows as coulomb’s constant.
Combining the two equations found;Fe (directly proportional to) q1q2 and Fe (Inversely proportional to) to the square of r
Coulomb’s law applies when
1) the charge on the 2 sphere are very small,
2) the two spheres are small compared to the distance between them.
^^ This way the charge distribution on the surface of the spheres will be fairly uniform.
When does coulomb’s law apply?
then the force measured between the 2 spheres is the same as if all the charge on each sphere is concentrated at the centre, this is also the reason why we measure r from the centre of each sphere.
What if the charge distribution is uniformly distributed
Coulomb’s law is extremely accurate when using POINT CHARGES, it is reasonably accurate when the spheres are small.
Extreme accuracy and reasonable accuracy of the coulomb’s law
It id due to the presence of the second charged sphere that causes the charge on the surface of each sphere to redirect so r can no longer be measure from the centre of the spheres.
WHEN THE SPHERES ARE SMALL, the charge distribution stays nearly uniform due tot he strong repulsive forces between the charged on each sphere.<<< this is only true if the distance between the two spheres large compared to the size of the spheres.
What is the difference in accuracy due to?
the force between 2 point charges is inversely proportional to the square of the distance between the charges and directly proportional to the product of the charges.
Coulomb’s law
1) Both are inverse square laws that are also proportional to the product of quantities that characterize the bodies involved.
2) Forces act along the line joining the two centres of the masses or charges.
3) The magnitude of force is accurately given by the force that would be measured if all the mass or charge is concentrated at a point at the centre of the sphere.
Coulomb’s law vs Newton’s third law
1) The gravitational force can only attract while the electric force can attract or repel.
2) The universal gravitational constant is very small, while coulomb’s constant is very large.
Coulomb’s law vs Newton’s third law
The value of proportionality constant, k can be determined using a torsional balance similar to that used by Cavendish. By placing charges of known magnitude a given distance apart and measuring the resulting angle of twist in the suspending wire, we can ind the value for the electric force causing the twist. The use coulomb’s law in the form:
k= (Fe*r^2)/(q1*q2)
to determine the rough value of k.
Proportionality constant
9.0 * 10^9 N.m^2/C^2
Proportionality constant

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