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

Many students find this pair of formula too abstract. Hopefully this video gives you a solid and intuitive feel.

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

https://youtu.be/wMeBlxbvFLg&rel=0

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

https://youtu.be/HWE4XjV-NlU&rel=0

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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

Do you know what is elevation or altitude? E.g. Bukit Timah hill has an elevation of 164 m above sea level. The lowest point of the Dead Sea is 413 m below sea level. You can think of electric potential as the “elevation” of the “electric landscape”.

https://youtu.be/XPxc7IWE-9o&rel=0

Coulomb’s law: F_e=kQ₁Q₂/d²

Newton’s law of gravitation: F_g=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,  is a much larger constant than . 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.

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.

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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.

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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).