How does the displacement current term in Ampere-Maxwell law help explain charging a capacitor?

How does the displacement current term in Ampere-Maxwell law help explain charging a capacitor?

• A. It introduces a physical current between plates that completes the loop.
• B. It accounts for changing electric field between plates, making ∮ B · dl continuous when there is no physical current.
• C. It cancels the magnetic field produced by the current wire.
• D. It only exists in AC circuits.

Answer: (B)

When a capacitor charges, conduction current flows in the wires, but there is no actual charge moving through the space between the plates. If you use Ampere’s law without modification, the magnetic field around a loop that passes through the gap would seem to depend on whether there’s a real current crossing that surface, which would break the consistency as the capacitor charges. The displacement current term, ε0 dΦE/dt, captures the changing electric field between the plates. This term acts like a current in how it influences the magnetic field, even though no charges move in the gap. So the total current through a surface bounded by a closed loop includes both the conduction current and this displacement current, making ∮ B · dl continuous and consistent during charging. In other words, the changing electric flux between plates creates a magnetic effect just like a real current, preserving Ampere-Maxwell law in all parts of the circuit.

When a capacitor charges, conduction current flows in the wires, but there is no actual charge moving through the space between the plates. If you use Ampere’s law without modification, the magnetic field around a loop that passes through the gap would seem to depend on whether there’s a real current crossing that surface, which would break the consistency as the capacitor charges. The displacement current term, ε0 dΦE/dt, captures the changing electric field between the plates. This term acts like a current in how it influences the magnetic field, even though no charges move in the gap. So the total current through a surface bounded by a closed loop includes both the conduction current and this displacement current, making ∮ B · dl continuous and consistent during charging. In other words, the changing electric flux between plates creates a magnetic effect just like a real current, preserving Ampere-Maxwell law in all parts of the circuit.