Question

The varying electric fields are a source of

• A. Displacement current
• B. Conduction current
• C. Convection current
• D. Both conduction and convection current

Hint:

Maxwell's correction led to the final version of the Maxwell-Ampere equation, which accounts for both current components: \[ \oint \vec{B} \cdot d\vec{\ell} = \mu_0 \left( I_c + I_d \right) = \mu_0 I_c + \mu_0 \epsilon \frac{d\Phi_E}{dt} \] This unification explains how electromagnetic waves can self-propagate through a vacuum without needing a physical medium!

Answer 1

The Correct Option is A

Concept: In classical electromagnetism, Ampere's original circuital law related the line integral of a magnetic field around a closed loop directly to the conduction current passing through the enclosed surface: \[ \oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_c \] However, James Clerk Maxwell identified a mathematical inconsistency in this law when applying it to time-varying circuits, such as a capacitor charging or discharging in an AC loop. While charge physically flows through the connecting wires as a conduction current ($I_c$), no actual charge carriers cross the insulating dielectric gap between the capacitor plates. Yet, a real magnetic field is still generated in that gap. To resolve this issue and satisfy the continuity equation for charge preservation ($\nabla \cdot \vec{J} = -\frac{\partial \rho}{\partial t}$), Maxwell postulated the existence of a new current term termed the Displacement Current ($I_d$). Mathematical Formulation of Displacement Current: The displacement current is not caused by the physical motion of actual charged particles. Instead, it is a term proportional to the time rate of change of the electric flux ($\Phi_E$) or the electric displacement field ($\vec{D}$): \[ I_d = \epsilon \frac{d\Phi_E}{dt} = \int \frac{\partial \vec{D}}{\partial t} \cdot d\vec{A} \] Where $\vec{D} = \epsilon \vec{E}$. This means that a time-varying, changing electric field ($\frac{\partial \vec{E}}{\partial t} \neq 0$) acts as an effective current source that produces a surrounding magnetic field, exactly like a physical current does. Review of alternative current terms:
• Conduction Current ($I_c$): The actual physical flow of free charge carriers (such as electrons in a metal conductor) driven by an electric field, following Ohm's Law: $\vec{J} = \sigma \vec{E}$.
• Convection Current: The physical motion of bulk charged masses through a vacuum or fluid medium without relying on a conducting material lattice (such as an electron beam in a CRT tube). Thus, a varying electric field is specifically the source of the displacement current, matching Option (1).