Maxwell’s Equations (so far…) Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law *Not complete
Something is missing in Ampere’s Law
A capacitor, connected to a circuit Side view
A capacitor, connected to a circuit Side view
A capacitor, connected to a circuit Side view
These answers can’t both be right! Something missing here… These answers can’t both be right!
Faraday found that time-varying magnetic fields are accompanied by electric fields. Maybe time-varying electric fields are also accompanied by magnetic fields?... James Clerk Maxwell (1831 – 1879)
The electric field between the plates is changing in time, as the capacitor is charged. Field inside a capacitor: Electric flux:
The electric field between the plates is changing in time, as the capacitor is charged. Field inside a capacitor: Electric flux:
The electric field between the plates is changing in time, as the capacitor is charged. Field inside a capacitor: Rate of change of the flux: (since i = dq/dt)
The electric field between the plates is changing in time, as the capacitor is charged. Field inside a capacitor: Result:
This is a relationship between the changing electric flux inside the capacitor, and the current outside the capacitor.
Maxwell used it to fix Ampere’s Law:
Maxwell used it to fix Ampere’s Law:
Ampere-Maxwell Law This is the last of Maxwell’s equations.
Now the answers are the same.
Maxwell’s Equations (so far…) Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law *Not complete
Maxwell’s Equations Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law Ampere-Maxwell Law
Maxwell’s Equations in empty space No charge: q = 0 No currents: i = 0
Maxwell’s Equations in empty space Even with no charges or currents nearby, time-varying electric and magnetic fields can exist… as travelling waves.
Maxwell’s equations predict travelling waves.
Maxwell’s equations predict travelling waves.
Maxwell’s equations predict travelling waves.
Maxwell’s equations predict light.