Ampere's Law and Capacitor Charging

Ampere's Law Limitations

• Ampere's law, stating that the circulation of a magnetic field along a closed loop equals the product of the permeability of free space and the enclosed current, is not universally applicable.
• It fails to accurately predict magnetic fields in situations like charging or discharging capacitors.

Capacitor Charging and Magnetic Fields

• Capacitor charging increases the electric field and electric flux between its plates.
• Experiments show a non-zero magnetic field between the capacitor plates, despite no real current flowing there.
• Ampere's law predicts zero magnetic field in this situation, highlighting its inadequacy.

Maxwell's Contribution: Displacement Current

• Maxwell recognized that changing electric fluxes can induce magnetic fields, analogous to changing magnetic fluxes inducing electric fields (Faraday's law).
• This required another source of magnetic field beyond real currents.
• He introduced displacement current to amend Ampere's law.
• Displacement current equals ε₀ (dΦ_E/dt), where ε₀ is the permittivity of free space and dΦ_E/dt is the rate of change of electric flux.

Ampere-Maxwell's Law

• Ampere-Maxwell's law combines real current and displacement current.
• It states that the circulation of the magnetic field around a closed loop equals the sum of enclosed real current and displacement current through the surface bounded by the loop.

Significance of Displacement Current

• Displacement current is a theoretical concept explaining magnetic fields arising from changing electric fields, crucial where no real current exists.
• It connects electric and magnetic fields, showcasing their interdependence.
• The unit of displacement current is the ampere, similar to real current, indicating its contribution to the magnetic field.
• This concept unified electricity and magnetism, a significant advance in electromagnetism.