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Coulomb's law

# Coulomb's law and electric force review

Review your understanding of Coulomb's law and electric forces in this free article aligned to NGSS standards.

## Key terms

TermMeaning
Electric chargeA property of matter that determines the force on the object when placed in an electromagnetic field. Objects can have positive, negative, or neutral charge. Like energy and matter, total electric charge is conserved, and charge cannot be created or destroyed.
kThe electric force constant, or Coulomb’s constant, which has a value of 9, point, 0, start text, x, end text, 10, start superscript, 9, end superscript, start fraction, start text, N, end text, dot, start text, m, end text, squared, divided by, start text, C, end text, squared, end fraction.

## Equations

EquationSymbol breakdownMeaning in words
open vertical bar, F, start subscript, E, end subscript, close vertical bar, equals, k, open vertical bar, start fraction, q, start subscript, 1, end subscript, q, start subscript, 2, end subscript, divided by, r, squared, end fraction, close vertical barF, start subscript, E, end subscript is electric force, k is the Coulomb’s law constant, q, start subscript, 1, end subscript and q, start subscript, 2, end subscript are the charges, and r is the distance between the charges.The magnitude of the electric force between q, start subscript, 1, end subscript and q, start subscript, 2, end subscript is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them. This equation is known as Coulomb’s Law.

## Comparing electric force and gravitational force

Coulomb's law may look somewhat familiar, because it has a lot in common with Newton's law of gravitation:
\begin {aligned} |{F_E}| &= k \left | \dfrac{q_1 q_2}{r^2} \right | \\\\ |{F_g}| &= G\dfrac{ m_1 m_2}{r^2} \end{aligned}
Like gravitational force, whose magnitude increases with mass, electric force magnitude increases with the magnitude of the charges. Both forces act along the imaginary line joining the objects. Both forces are inversely proportional to the square of the distance between the objects, this is known as the inverse-square law. Also, both forces have proportionality constants. F, start subscript, g, end subscript uses G and F, start subscript, E, end subscript uses k, where k, equals, 9, point, 0, times, 10, start superscript, 9, end superscript, start fraction, start text, N, end text, dot, start text, m, end text, squared, divided by, start text, C, end text, squared, end fraction.
A difference between gravitational force and electric force is their relative strengths, related to the ratio of k to G. The electrostatic force between an electron and a proton is many orders of magnitude greater than the gravitational force between them.

## Direction of electric force

The electric force F, start subscript, E, end subscript can be either attractive or repulsive. Opposite charges, such as a positive charge and a negative charge, attract each other. Like charges, such as two negative charges or two positive charges, will repel each other.
Figure 1. Opposite charges attract each other.
Figure 2. Like charges repel each other.

## What else should I know about Coulomb's law?

• Electric force is inversely proportional to r, squared instead of r. As the distance between charges increases, the electric force decreases by a factor of start fraction, 1, divided by, r, squared, end fraction. For example, if we double the distance between the two electrons, the repulsive force between them would reduce (because it is inverse), and it would go down by a factor of 4 instead of 2 (because of the square).