Physic Labs

Electricity and magnetism

Electric charge and Coulomb’s law

Like charges repel and unlike charges attract; the force between point charges falls with the square of their separation.

Electric charge is a property of matter that gives rise to electric interactions. Charge comes in positive and negative signs. Experiments show that like charges repel and unlike charges attract; total charge is conserved in an isolated system.

F=k ∣q1q2∣r2,k=14πε0≈8.99×109 N m2/C2F = k\,\frac{|q_1q_2|}{r^2}, \qquad k=\frac{1}{4\pi\varepsilon_0}\approx 8.99\times10^9\ {\rm N\,m^2/C^2}

Definition: Charge and electric force

Charge qq is measured in coulombs (C), and rr is the distance between two point charges. Coulomb’s law gives the force magnitude in vacuum (and approximately in air). The force lies along the line joining the charges; their signs determine attraction or repulsion.

Change charge signs, magnitudes, and separation to explore attraction, repulsion, and the inverse-square law.

How does distance matter?

With both charges fixed, doubling their separation reduces the force to one quarter. Tripling either charge triples the force. These statements concern magnitude; charge signs still set the force direction.

Example: Force between two charges

Two charges, +2.0 μ+2.0\,\muC and −3.0 μ-3.0\,\muC, are 0.200.20 m apart in air. Find the force magnitude and identify the interaction.

Solution

F=8.99×109(2.0×10−6)(3.0×10−6)/(0.20)2≈1.35F=8.99\times10^9(2.0\times10^{-6})(3.0\times10^{-6})/(0.20)^2\approx1.35 N. The signs are opposite, so the force is attractive.

Check the scaling by holding one charge fixed and comparing two measurements. If a separation of 0.300.30 m is reduced to 0.150.15 m, the force becomes four times larger because r2r^2 falls to one quarter. In a uniform dielectric, the interaction is weaker than in vacuum; the relative permittivity εr\varepsilon_r increases the effective denominator. The point-charge model is appropriate when object sizes are much smaller than their separation.

Charge is also quantized: an ordinary object's net charge is an integer multiple of the elementary charge in magnitude. Rubbing transfers electrons between objects, while total charge remains conserved.

Quick check

If the separation is doubled while both charges stay fixed, what happens to the Coulomb-force magnitude?

How do two point charges with opposite signs interact?

References

  1. Young, Freedman (2019). University Physics
  2. Halliday, Resnick, Walker (2014). Fundamentals of Physics