# UY1: Electric Charge & Coulomb’s Law

There are exactly two kinds of electric charge: negative and positive.

Electric charge is quantized:

The magnitude e of charge of the electron or proton is a natural unit of charge. Every observable amount of electric charge Q is always an integer multiple n of this basic unit e:

$$Q = ne$$

Principle of conservation of charge:

The algebraic sum of all the electric charges in any closed system is constant.

Opposite charges attract, and like charges repel

A positive charge and a negative charge attract each other. Two positive charges or two negative charges repel each other.

The magnitude of the electric force F between two point charges, q1 and q2, is directly proportional to the product of the charges and inversely proportional to the square of the distance r between them:

$$F = k \frac{|q_{1} q_{2} |}{r^{2}}$$

The directions of the forces the two charges exert on each other are always along the line joining them.

$$\vec{F}_{2 \, \text{on} \, 1} = \, – \vec{F}_{1 \, \text{on} \, 2}$$

The value of the proportionality constant k depends on the system of units used.

In SI units:

$$k = \frac{1}{4 \pi \epsilon_{0}} \approx 8.988 \times 10^{9} \, Nm^{2} C^{-2}$$

, where the permittivity of free space:

$$\epsilon_{0} \approx 8.854 \times 10^{-12} \, N^{-1}m^{-2} C^{2}$$

The SI unit of electric charge is called one coulomb:

$$1 C = 1 \, As$$

, where ampere A is a unit of electric current, equal to one coulomb per second.

Principle of superposition of forces:

When two charges exert forces simultaneously on a third charge, the total force acting on that charge is the vector sum of the forces that the two charges would exert individually.

Next: The Electric Field As A Web

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