Electrostatics

Coulomb's Law

Like charges repel and opposite charges attract with a force following an inverse-square law: $F = \frac{kq_1q_2}{r^2}$ with $k \approx 9 \times 10^9\ \text{N·m}^2/\text{C}^2$. Charge is quantized in units of $e = 1.6 \times 10^{-19}\ \text{C}$ and conserved. Doubling separation cuts the force to one quarter — the MCAT loves this scaling.

Electric Field and Potential

The field is force per unit positive charge, $E = F/q = kq/r^2$, pointing away from positive and toward negative charges. Electric potential is energy per charge: $V = \frac{kq}{r}$ Potential is a scalar (add algebraically); field is a vector (add by components). A uniform field between parallel plates satisfies $E = V/d$.

Potential Energy and Charge Motion

The energy of a charge at potential $V$ is $U = qV$ Positive charges accelerate from high to low potential; negative charges do the opposite — both move toward lower potential energy. Equipotential surfaces are everywhere perpendicular to field lines, and moving a charge along one costs zero work.

Key Takeaways

• Inverse-square scaling with distance governs both force and field.
• Potential adds as a scalar; field adds as a vector.
• Work done by the field equals $q\Delta V$ and is path-independent.
• No work is required to move charge along an equipotential.