Category: 12 Electric Field

Electric vs Gravitation

Coulomb’s law: Fe=kQ1Q2/d2

Newton’s law of gravitation: Fg=GM1M2/d2

The similarities between Newton’s law of gravitation and Coulomb’s Law are hard to miss. But there is one major difference between them: while there is only one type of mass, there are two types of charges: positive and negative. While all gravitational forces are attractive, electric forces is attractive between two unlike charges, but repulsive between two like charges. And this has made all the difference.

If you think about it, k=\frac{1}{4\pi {{\varepsilon }_{0}}}=8.99\times {{10}^{9}}\text{ N }{{\text{m}}^{2}}\text{ }{{\text{C}}^{-2}} is a much larger constant than G=6.67\times {{10}^{-11}}\text{ N }{{\text{m}}^{2}}\text{ k}{{\text{g}}^{-2}}. In addition, one mole of electrons make up a charge of ~104 C but only a mass of ~10-4 kg. So the obvious question is: shouldn’t electrical forces always dominate over gravitational forces under all situations?

Well, we have to realize that it is very difficult to hold a large amount of unbalanced charges in a small volume because LIKE CHARGES REPEL. Gravitation has no such problem since it is always attractive. For this reason,

  • Gravitational forces dominate the study of astronomy. Massive stars planets can be formed through gravitational pulls. The orbits of planets and comets are also governed by gravitational forces. Heavenly bodies, even though they contain lost of electrons and protons, are neutral in charge to one another.
  • Electric forces dominate the study of chemistry. At atomic distances, the localised charges of electrons and ions provide the binding forces for the formation of molecules. Electric attraction AND repulsion provide the explanations for the properties of solids, liquids and gases. The gravitational attraction between the mass of individual electrons and ions are negligible.

It’s all electric

Do you realize that chemical bonds, whether intra-molecular and inter-molecular, are electrical in nature?

For example, the ionic bonds that hold a sodium chloride crystal together are basically the electrical forces of attraction between the Na+ ions and Cl ions.

The hydrogen bonds that keep the H2O molecules in a drop of water from flying apart are basically the electrical force of attraction between the partially positively charged hydrogen atom of one H2O molecule with the partially negatively charged oxygen atom of another H2O molecule.

On the other hand, when atoms or molecules come too close together, electrical repulsion will set in. This could be due to the mutual repulsion between the electron clouds, or in more extreme situations the mutual repulsion between the nuclei.

The so called “contact force” between touching surfaces, is also electrical in nature. The electrical repulsion between (the electron clouds of) the atoms of your butt and the chair you’re sitting on is the reason you are not falling through the chair. Technically, your butt is hovering above the chair (by a separation of the scale of 10-10 m).

12.6 Electric Field Map

The one difference between homo sapiens and other animals is that we are able to imagine things that do not exist. Physicists especially are full of imaginations. First, we imagine electric fields and electric potentials. Then we draw field patterns consisting of field lines and equipotential lines to help us visualize our own imagination.

Just like iron filings can be used to “show” magnetic field lines, grass seeds can be used to “show” electric field lines. Just keep in mind that field lines are not physical objects. They are figments of our imagination.

In practice, we usually map out the equipotential lines first, before we can map out the electric field lines.

Why must electric field lines cut the equipotential lines cut perpendicularly? The video below answers this FAQ.

12.4.1 Electric Potential of a Point Charge

A positive point charge creates an “electric mountain” around it. A negative point charge creates an “electric crater” around it.

Here is an worked example on how to calculate the resultant electric potential.

Applets:

This applet can be used to illustrate the field and potential set up by point charges and more.

Falstad vector (field visualisation): Click HERE