Electric Force and Coulomb's Law

Electric force, also called electrostatic force, is the push or pull that two charged objects exert on each other simply because they carry charge. It is one of the fundamental forces you study in physics, and it explains everything from why a balloon sticks to a wall after rubbing it on your hair to how atoms hold together. Unlike gravity, which is always attractive, electric force can either pull charges together or push them apart, depending on the sign of the charges involved.

The size of the electric force between two point charges is given by Coulomb's law:

\( F = k \dfrac{|q_1 q_2|}{r^2} \)

Here, \(F\) is the magnitude of the electric force in newtons, \(q_1\) and \(q_2\) are the magnitudes of the two charges in coulombs, \(r\) is the distance between the centers of the charges in meters, and \(k\) is Coulomb's constant. This formula tells you two important things at a glance: force grows larger when the charges are bigger, and it shrinks quickly as the charges move apart, since \(r\) is squared in the denominator.

Coulomb's constant has the value \( k \approx 8.99 \times 10^9 \ \)N\( \cdot \)m\(^2/\)C\(^2 \). This number converts the product of two charges and the inverse square of their distance into a force you can measure in newtons. Because \(k\) is so large, even tiny charges (measured in microcoulombs or nanocoulombs) can produce noticeable forces when they are close together.

Coulomb's law gives you the magnitude of the force, but the direction depends on the signs of the charges:

• Two like charges (both positive or both negative) repel each other, pushing apart along the line connecting them.
• Two unlike charges (one positive and one negative) attract each other, pulling together along that same line.

In both cases, the force acts along the straight line joining the two charges, and by Newton's third law, each charge feels a force of equal magnitude but opposite direction from the other.

Suppose \(q_1 = 2 \times 10^{-6}\ \)C\(\) and \(q_2 = 3 \times 10^{-6}\ \)C\(\) are separated by \(r = 0.5\ \)m\(\). Find the electric force between them.

\( F = k \dfrac{|q_1 q_2|}{r^2} = (8.99 \times 10^9) \dfrac{(2 \times 10^{-6})(3 \times 10^{-6})}{(0.5)^2} \)

\( F = (8.99 \times 10^9) \dfrac{6 \times 10^{-12}}{0.25} \approx 0.216\ \)N\( \)

Since both charges are positive, this force is repulsive: each charge pushes the other directly away along the line between them. If one of the charges were negative instead, the same calculation would give the same magnitude, but the force would be attractive.

Because Coulomb's law involves \(r^2\) in the denominator, electric force is very sensitive to distance. Doubling the distance between two charges cuts the force to one quarter of its original value, and tripling the distance reduces it to one ninth. Doubling either charge, on the other hand, simply doubles the force, since the numerator depends linearly on each charge.

When more than two charges are present, the total electric force on any one charge is the vector sum of the individual forces from every other charge, calculated separately with Coulomb's law and then added as vectors. This is called the superposition principle, and it lets you break complicated arrangements of charges into simple pairwise calculations.

Electric force describes the direct interaction between two specific charges, while an electric field describes the influence a charge creates in the space around it, independent of any second charge being present. Once you know the field at a point, you can find the force on any charge placed there. Electric force is also closely tied to electric potential and electric potential energy, which describe the energy associated with moving a charge within that field.

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