What is “electronic charge”? Why there are two kinds of charges? Why do the same charges repel, and dissimilar charges attract each other? Why does their behavior agree with Coulomb’s Law? These are among the most basic questions of physics. Let us assume the existence of a kind of microparticle in the universe, which we can call an electon for our purposes here. Three situations are possible: if an object contains a surplus of electons, it will be positively charged; if a deficit of electons, it will be negatively charged; if an object contains electons equal to its expected value, in the saturated state, it is neutral. The charged objects, containing these electons, have the ability to exchange charged or uncharged microparticles in order to achieve a neutral state. The acting force between two charged objects comes from the exchange of charged and uncharged microparticles. The same charges repel, and dissimilar charges attract each other. The value of force is consistent with Coulomb’s Law. The material homogeneous between two charged objects affects the value of the acting force between them, but does not affect the direction.
Coulomb is perhaps most famous for the law of physics bearing his name. Coulomb’s law describes the relationship between force, charge and distance. In 1785, Coulomb published a paper describing the torsion balance. This paper would become the first of a series of seven papers that Coulomb would have published on the topics of magnetism and electricity. The torsion balance allowed Coulomb to make more precise measurements of force than anyone prior to that time.
Coulomb’s law says the electrical force between two charges (q1) and (q2) is proportional to the product of the two charges divided by the distance between the two charges squared (see Equation 1 above). The torsion balance which Coulomb invented, allowed him to accurately measure electric forces and thereby establish this relationship. Since the charges q can be either positive or negative, Coulomb’s law implies that the resultant force can be either attractive or repulsive.
Example Problem:
Two neutrally charged bodies are separated by 1 cm. Electrons are removed from one body and placed on the second body until a force of 1×10-6 N is generated between them. How many electrons were transferred between the bodies?
Solution:
First, draw a force diagram of the problem.
Define the variables:
F = coulomb force = 1×10-6 N
q1 = charge on first body
q2 = charge on second body
e = charge of a single electron = 1.60×10-19 C
k = 8.99×109 N•m2/C2
r = distance between two bodies = 1 cm = 0.01 m
Start with the Coulomb’s Law equation.
As an electron is transferred from body 1 to body 2, body 1 becomes positive and body two becomes negative by the charge of one electron. Once the final desired force is reached, n electrons have been transferred.
q1 = +ne
q2 = -ne
The signs of the charges give the direction of the force, we are more interested in the magnitude of the force. The magnitude of the charges are identical, so we can ignore the negative sign on q2. This simplifies the above equation to:
We want the number of electrons, so solve the equation for n.
Substitute in the known values. Remember to convert 1 cm to 0.01 m to keep the units consistent.
n = 6.59×108
Answer:
6.59×108 electrons were transferred between the two bodies to produce an attractive force of 1×10-6 Newtons.
Why Don’t Electrons Just Fall Into the Nucleus of an Atom?
The electron, approaching the proton, will have kinetic energy and potential energy. When it is far away, it will have a relatively huge amount of potential energy, the same way objects raised high above the ground have huge amounts of potential energy. As it moves towards the proton, it loses some of that potential energy. Some of it is radiated away, as electromagnetic energy. Some of it is converted to kinetic energy. Kinetic energy keeps an electron hopping, and keeps it from staying in a nucleus and combining with a proton.
Combine a proton and an electron, and charge-wise, you’ve made a neutron. That’s what should happen if electrons fell into a nucleus. A proton’s mass is 1.6726 x 10-27 kg, and an electron’s mass is 0.00091 x 10-27 kg, but a neutron’s mass is 1.6749 x 10-27 kg. So the mass of an electron and proton combined is still nowhere near enough for a neutron. If you want them to combine together, you would need to add energy, or mass, or both.
Coulomb’s law holds even within atoms, correctly describing the force between the positively charged atomic nucleus and each of the negatively charged electrons. This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between ions increases, the force of attraction, and binding energy, approach zero and ionic bonding is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable.
Jang The Great 