No. 0426 November 2025.
EM fields and waves, EE2147: my electrostatics notes
From one force to a field: Coulomb’s law, added up
My electrostatics notes run from Coulomb’s law to one boxed line. As a vector, the law points along the line between two charges and falls off with the square of the distance between them. With many charges the forces on a test charge Q add, and Q comes out of the sum as a common factor. What is left depends only on where Q sits: that is the electric field.
F12 = Q1Q2 (r2 − r1) / 4πε0 |r2 − r1|³
F = (Q / 4πε0) Σk Qk (r − rk) / |r − rk|³⇒E(r) = F / Q
With 1/4πε0 ≈ 8.99 × 10⁹ N m² C⁻², from ε0 ≈ 8.854 × 10⁻¹² F m⁻¹, the field comes out in newtons per coulomb, the same unit as volts per metre. One line in my notes was marked TODO: F12 = −F21. Swapping the labels turns r2 − r1 into r1 − r2 and leaves the distance alone, so the force reverses and keeps its size. Newton’s third law falls out of the formula.
what I don’t understand yet
Gauss’s law. My notes have its heading and nothing under it yet. The course asks for Laplace’s and Poisson’s equations to be derived from it, and I want to reach them from this sum rather than quote them.
where this goes
The field is minus the gradient of a potential, E = −∇V, which is why entry 05 is about gradients.