Displacement Current and Maxwell's Equations
Ampere's law fails for a charging capacitor until a term for changing electric flux is added, and with it the four equations close on each other. They say that changing fields of either kind make the other.
What a learner can do afterwards
- Shows where Ampere's law breaks down between capacitor plates and what the extra term fixes
- States all four equations in words and names the physical content of each
- Explains why the set is symmetric except for the absence of magnetic charge
1 · Read
Ring a charging capacitor with a loop and Ampere's law breaks: no conduction current crosses the gap, yet the loop rule demands one. The fix is the changing electric field between the plates, which acts exactly like a current. This displacement current is mu0 eps0 times the rate of change of electric flux. Add it to the loop rule and the contradiction heals, completing the symmetry between electricity and magnetism.
The full set is four statements. Gauss for E: charges source electric fields. Gauss for magnetism: there is no magnetic charge. Faraday: changing magnetic flux rings the region with electric field. Ampere-Maxwell: currents plus changing electric flux ring it with magnetic field. The two change equations feed each other, changing E birthing B birthing E, and the pair propagates as a wave at 1 over sqrt(mu0 eps0). That speed equals the measured speed of light, and Hertz later confirmed the waves with spark-gap antennas.
The set is almost symmetric, except one side lacks a source. Electric charges exist alone, but magnetic poles always come in north-south pairs, so the magnetic Gauss law reports zero source. A magnetic monopole would complete the mirror, but none has ever been found. State the four laws in words first; the missing monopole is the one lopsided detail to keep.
Answer which-equation questions with this map. Sources of E mean Gauss for E. No monopole means Gauss for magnetism. Changing B means Faraday. Currents or changing E mean Ampere-Maxwell. And remember the hardware moral: an accelerated charge sheds linked E and B ripples that feed each other outward, which is how every transmitter broadcasts and every receiver listens.
Changing electric flux repairs Ampere's law as displacement current, the four laws close into light-speed waves, and only the missing monopole spoils the symmetry.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.