recall and use Coulomb’s law F = Q1Q2 / (4πε0 r 2) for the force between two point charges in free space

Uniform Electric Fields 📐

What is a Uniform Electric Field?

A uniform electric field is one where the electric field strength (E) is the same at every point in space. Think of it like a set of parallel invisible lines that push charged particles in the same direction, just like a steady wind blowing across a field of flags. The field lines are straight and evenly spaced, indicating that the force on a charge would be the same no matter where it is in the field.

Coulomb’s Law – The Force Between Two Point Charges

Coulomb’s law tells us how strong the force is between two point charges. It’s the “rule of thumb” for electric forces in free space.

Formula:

\$F = \frac{Q1 Q2}{4 \pi \varepsilon_0 r^2}\$

  • \$Q1\$ and \$Q2\$ are the charges (in coulombs).
  • \$r\$ is the distance between the charges (in metres).
  • \$\varepsilon_0\$ is the vacuum permittivity, a constant ≈ \$8.85 \times 10^{-12}\$ F/m.

Quick Recap Box

Remember: The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The sign of the force (attractive or repulsive) depends on whether the charges are like or unlike.

Example Problem 👩‍🏫

  1. Two point charges: \$Q1 = +3\,\mu\text{C}\$ and \$Q2 = -2\,\mu\text{C}\$.
  2. The distance between them is \$r = 0.05\,\text{m}\$.
  3. Calculate the magnitude of the force.
  4. Determine whether the force is attractive or repulsive.

Solution:

First, convert microcoulombs to coulombs: \$3\,\mu\text{C} = 3\times10^{-6}\,\text{C}\$, \$-2\,\mu\text{C} = -2\times10^{-6}\,\text{C}\$.

Plug into Coulomb’s law:

\$F = \frac{(3\times10^{-6})(-2\times10^{-6})}{4\pi(8.85\times10^{-12})(0.05)^2}\$

\$F \approx -\frac{6\times10^{-12}}{4\pi(8.85\times10^{-12})(0.0025)} \approx -\frac{6\times10^{-12}}{2.78\times10^{-10}} \approx -0.0216\,\text{N}\$

The negative sign indicates an attractive force (since the charges are opposite). The magnitude is about \$0.022\,\text{N}\$.

Table of Common Charge Combinations

\$Q_1\$ (C)\$Q_2\$ (C)\$r\$ (m)\$F\$ (N)
\$+1\times10^{-6}\$\$+1\times10^{-6}\$0.01\$0.009\$
\$-2\times10^{-6}\$\$+3\times10^{-6}\$0.02\$-0.015\$
\$+5\times10^{-6}\$\$-5\times10^{-6}\$0.05\$-0.022\$

Exam Tips & Tricks 🎓

  • Always check units: charges in coulombs, distance in metres, force in newtons.
  • Remember the sign of the force: same signs → repulsive (positive force), opposite signs → attractive (negative force).
  • When given microcoulombs, convert to coulombs before plugging into the formula.
  • Use the square of the distance: \$r^2\$ – a small change in distance can drastically change the force.
  • For quick estimates, you can ignore the constant \$4\pi\varepsilon_0\$ if you’re just comparing relative magnitudes.
  • Draw a diagram: label charges, distance, and direction of force to avoid confusion.