Electric Charges, Forces and Fields

Electric Charge

Static electricity is electric charge at rest, and there are many every day effects which are due to this. It is well known that if you wear a woollen jumper over a nylon blouse small sparks can be made when you take it off. A piece of polythene rubbed with a duster will attract small pieces of paper. A plastic comb rubbed with a cloth will make someone's hair stand on end if placed near it, a balloon rubbed on a jumper can be made to stick to the wall and television screens get charged and collect dust on them. Cling film, book covering film and sellotape can become charged as they are stripped or pulled off the reel. The mist from a waterfall is charged and a firm making chocolates had to earth the trolleys as the chocolates had become charged!

Applications of electrostatics:
(a) electrostatic dust collectors
(b) electrostatic paint sprays
(c) a photocopier

Electrostatics was probably discovered by Thales in about 600 BC and to detect static charge we usually investigate the electric field it produces or else discharge the charged body and observe the current it produces (this is usually small but think about lightning!) Gilbert (1540-1603) found that he could not charge conducting objects but in 1734 du Fay succeeded in doing this by using an insulating handle. In 1729 Gray found that charged object could be discharged through the human body to the ground thus giving the idea of conductors and insulators.

In 1745 du Fay discovered that there were just two types of static charge, positive and negative, and no more. This was later confirmed by Benjamin Franklin (1706-1790).

Static charges can be produced by the friction between two bodies. Two simple sources of positive and negative charge are:
Positive - glass after being rubbed with silk
Positive - cellulose acetate after being rubbed with a duster
Negative - polythene after being rubbed with a duster.
In each case the silk and duster acquires the opposite charge to the solid.

All electric charges exert a force on each other. This force can be either attractive or repulsive depending on the sign of the charge.

Two like charges repel each other while two unlike charges attract each other.

The effect of two charges on each other may be investigated by hanging up two graphite coated table tennis balls by threads (Figure 1) or by suspending a polythene rod in a cradle hanging from a fine thread and bringing another charged rod (of either sign) close to it. Alternatively small pieces of paper can be placed on the dome of a Van de Graaff generator. When the generator is switched on the paper flies off – they all have charges of the same sign and the same sign as the dome itself.

Remember that this is the same coulomb mentioned in current electricity where one amp is one coulomb flowing past a point in the circuit per second.

Electrostatic and gravitational forces - similarities and differences

We can compare the electrostatic force with that between two masses (F_G = Gm₁m₂/d²).
The two forces are similar in that:
(a) they are both inversely proportional to d²
(b) they depend on both the masses or both the charges
They differ in that:
(a) the gravitational force is always attractive but the electric force may be repulsive
(b) the gravitational force is independent of the material placed between the two masses while the electric force depends on the permittivity that material

Comparison between electric and gravitational forces in a hydrogen atom

We can now use our knowledge of gravitational and electric force to find out what is most important in holding atoms together. We will use the example of a hydrogen atom.

Gravitational force (F_G) = GMm/r² Electrostatic force (F_E) = (1/4πε_o)Q₁Q₂/d²

Now Q₁ = Q₂ since the charge on the electron is equal in size to the charge on the proton = 1.6x10^-19 C
Mass of a proton = 1.66x10^-27 kg and the mass of an electron = 9.1x10^-31 kg
So the ratio of the electrostatic force to the gravitational force within the hydrogen atom
= [(1/4πε_o)Q₁Q₂/r²]/GMm/r²
= [(1/4πε_o)Q₁Q₂]/GMm = 9x10⁹x(1.6x10^-19)²/6.67x10^-11x1.66x10^-27 x9.1x10^-31 = 2.3x10³⁹!
Clearly the electrostatic force is far more important in this case.

Example problems
1. Calculate the force between two charges - one of 5 C and the other of 25 mC placed 0.06 m apart in (a) helium.
(b) glycerol
Using:- F = (1/4πε)Q₁Q₂/d²
(a) ε_r = 1.00007 for helium F = 9x10⁹x5x25x10^-3/1.00007x(0.062) = 3.12x10¹¹ N
(b) ε_r = 43 for glycerol
F = 9x10⁹x5x25x10^-3/43x(0.062) = 7.26x10⁹ N

2. Two balls of mass 20 mg are each suspended in a vacuum from a non-conducting thread 0.5 m long. If the angle between the threads is 40^o calculate the charge on each ball.

Let the tension in each thread be T and the angle between the threads be 2A and so A = 20^o.
Horizontal forces :
Force between the charges = F = (1/4πε_o)Q₁Q₂/d² = 9x10⁹xQ²/d² = T sinA
Therefore sinA = 9x10⁹xQ²/Td²
but d/2 = 0.5sinA giving d = sin20 = 0.34
Vertical forces:
T cosA = mg = 20x10^-6x9.8 = 1.96x10^-4
Therefore: space cosA = 1.96x10^-4/T
Therefore: space tanA = (9x10⁹xQ²/0.342)/1.96x10^-4 = tan20 = 0.36
so Q² = 0.36x 1.96x10^-4x0.342/9x10⁹
Therefore the charge (Q) on each ball = 30 C