The total electric flux through any closed surface equals Q_enc/ε0. Electric field lines start on + charges and end on - charges.
II — Gauss's Law (Magnetic)
No magnetic monopoles
The total magnetic flux through any closed surface is always zero. B-field lines always form closed loops — no isolated north or south poles exist.
III — Faraday's Law
Changing B creates E
A changing magnetic flux through a loop induces an electromotive force (EMF). The induced E-field circulates around the changing B-field.
IV — Ampère-Maxwell Law
Currents & changing E create B
Magnetic fields are created by currents AND by changing electric flux (displacement current). This was Maxwell's key addition that unified E&M.
Electromagnetic Wave: E ⊥ B ⊥ propagation
Frequency (THz) 1.0
Amplitude 1.0
Maxwell's Equations Summary
I. Gauss (E): Charges → E II. Gauss (B): No monopoles III. Faraday: ΔB → E IV. Amp-Maxwell: I + ΔE → B ————————————————— c = 1/√(μ0ε0) = 2.998 × 10&sup8; m/s ————————————————— E and B oscillate ⊥ to each other and ⊥ to direction of propagation E/B = c (in vacuum)
Displacement Current
Maxwell added the displacement current term:
I_d = ε0 dΦ_E/dt
This makes Ampère's law consistent and predicts EM waves even in vacuum (no real current needed).
EM Spectrum
Radio → Microwave → IR → Visible → UV → X-ray → Gamma
All are EM waves, differing only in frequency.
Quick Quiz▼
1. Which equation says no magnetic monopoles exist?