Electric Charge: Definition, Properties, Formula (w/ Examples)

Electric charge is a fundamental physical property of matter and in particular, the subatomic particles protons and electrons. Just as atoms have mass, these particles have charge, and there is an electric force and electric field associated with this charge.

Properties of Electric Charge

Electric charge comes in two varieties: ​positive charge and negative charge​, which, like their names suggest, have opposite signs (unlike mass, which only has one variety). Objects with electrical charge exert an electric force on each other, just as objects with mass do via the gravitational force. But instead of always being an attractive force, as with mass, opposite charges attract while like charges repel.

The SI unit of charge is the coulomb (C). One coulomb is defined as the amount of charge that can be transferred by one ampere of electric current in one second. The fundamental charge carriers are the proton, with charge ​+e​, and the electron, with charge ​-e​, where the elementary charge ​e​ = 1.602 × 10-19 C.

The net charge on an object is the number of protons ​Np​ minus the number of electrons ​Ne​ times ​e​:

\text{net charge} = (N_p - N_e)e

Most atoms are electrically neutral, meaning that they have equal numbers of protons and electrons, so their net charge is 0 C. If an atom gains or loses electrons, it is called an ion and will have a nonzero net charge. Objects with net charge exhibit static electricity and can cling to each other as a result with a force dependent on the amount of charge.

Note that this transfer of electrons between atoms or between objects does not also result in significant change in mass of the objects. This is because, while protons and electrons have the same magnitude of charge, they have very different masses. The mass of an electron is 9.11 × 10-31 kg while the mass of a proton is 1.67 × 10-27 kg. A proton is more than 1,000 times heavier than an electron!

Coulomb's Law: Formula

Coulomb's Law gives the electrostatic force ​F​ between two charges, ​q1​ and ​q2​ a distance ​r​ apart:

F = k\frac{q_1q_2}{r^2}

Where ​k​ is the Coulomb constant = 8.99 × 109 Nm2/C2.

Note that this force is a ​vector,​ which points along a line directed away from the other particle if the charges are the same and toward the other particle if the charges are opposite.

Coulomb’s law, just like the force of gravity between two masses, is an inverse square law. This means that it decreases as the inverse square of the distance between two charges. In other words, charges that are twice as far apart experience a quarter the force. But while this charge diminishes with distance, it never goes to zero and so has infinite range.

Examples to Study

Example 1:​ A charge of +2​e​ and a charge of -4​e​ are separated by a distance of 0.25 cm. What is the magnitude of the Coulomb force between them?

Using Coulomb’s law, and being sure to convert cm to m, you get:

F = k\frac{q_1q_2}{r^2} = (8.99\times10^9)\frac{(2\times 1.602\times10^{-19})(-4\times 1.602\times 10^{-19})}{0.0025^2} = 2.95\times 10^{-22}\text{ N}

Example 2:​ Suppose an electron and proton are separated by a distance of 1 mm. How does the gravitational force between them compare to the electrostatic force?

The gravitational force can be computed from the equation:

F_{grav} = G\frac{m_pm_e}{r^2}

Where the gravitational constant ​G​ = 6.67 × 10-11 m3/kgs2.

Plugging in numbers gives:

F_{grav} = (6.67\times 10^{-11})\frac{(1.67\times 10^{-27})(9.11\times 10^{-31})}{(1\times 10^{-3})^2} = 1.015\times 10^{-61}\text{ N}

The electrostatic force is given by Coulomb’s law:

F_{elec} = k\frac{q_1q_2}{r^2} = (8.99\times10^9)\frac{(1.602\times 10^{-19})(-1.602\times 10^{-19})}{(1\times 10^{-3})^2} = 2.307\times 10^{-22}\text{ N}

The electrostatic force between the proton and electron is more than 1039 times greater than the gravitational force!

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