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
Draw a loop around a wire that feeds a charging capacitor. Ampere's law takes the current through any surface bounded by the loop. A flat surface cut by the wire gives I, but a bulging surface that passes between the plates meets no wire and gives zero. Maxwell fixed the clash: the changing electric flux between the plates acts like a current. Eps0 times its rate of change is the displacement current, so the loop rule gains mu0 eps0 times that rate.
The full set has four laws. Gauss for E: electric charges are the sources of electric field. Gauss for magnetism: the magnetic flux through any closed surface is zero, so there is no magnetic charge. Faraday: changing magnetic flux makes a curling electric field. Ampere-Maxwell: currents plus changing electric flux make a curling magnetic field.
The set is almost symmetric. Electric charges exist alone, but magnetic field lines have no beginning or end. Cut a bar magnet and each piece still has a north and a south pole. A lone pole, called a magnetic monopole, would give the magnetic Gauss law a source, but none has been found. That missing source is the one gap in the mirror between the electric and magnetic laws.
Match a question to its law. Sources of E point to Gauss for E. No magnetic charge points to Gauss for magnetism. Changing B points to Faraday. Currents or changing E point to Ampere-Maxwell.
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.
The rewritten readings were written for this dataset.
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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.