The charge build up in a capacitor is due to

Question

Examoogle · Accepted Answer

Option B: Displacement current density

Explanation & Concepts:
The charge buildup on capacitor plates in a time-varying field is driven by displacement current, as defined in Maxwell's modification to Ampere's Law. Even though no physical charge carriers cross the dielectric gap, the changing electric flux creates an effective current.

Working Principle: In a capacitor, the time-varying electric field $\vec{E}$ produces a changing electric flux density $\vec{D}$. Maxwell's fourth equation states that $
abla 	imes \vec{H} = \vec{J}_c + \frac{\partial\vec{D}}{\partial t}$. The term $\frac{\partial\vec{D}}{\partial t}$ represents the displacement current density ($J_d$), which accounts for the accumulation of charge on the metallic plates despite the presence of an insulating dielectric.

Key Formulas: $J_d = \frac{\partial\vec{D}}{\partial t}$ — Definition of displacement current density; $\vec{D} = \epsilon\vec{E}$ — Relationship between flux density and electric field

Key Points: Displacement current is not a flow of charge carriers like conduction current.; It is proportional to the time rate of change of the electric field intensity.; It allows the continuity of current in circuits containing capacitors.; It satisfies the condition for the continuity equation $
abla \cdot \vec{J} + \frac{\partial ho_v}{\partial t} = 0$.

Advantages: Enables existence of electromagnetic waves in free space; Essential for analyzing high-frequency circuit behavior

Disadvantages: Does not contribute to ohmic heating (Joule heating) in dielectrics; Often neglected in DC steady-state analysis

Applications: Electromagnetic wave propagation theory; Capacitor charge-discharge analysis in AC circuits

Additional Info: Conduction current density refers to the flow of free electrons in a conductor.. Magnetization describes the density of magnetic dipole moments in a material, which does not cause plate charge accumulation.. Polarization ($P$) refers to the alignment of dipoles in a dielectric, which is related to $D$ ($D = \epsilon_0 E + P$) but is distinct from the current causing charge transport.

Answer: B is correct — The displacement current density $\frac{\partial\vec{D}}{\partial t}$ provides a physical mechanism for the continuity of current through capacitors, resulting in the accumulation of charge.

Exam Tip: Remember that displacement current is the vital link that makes Maxwell's equations consistent with the charge conservation principle ($\nabla \cdot \vec{J} = -\frac{\partial \rho}{\partial t}$).

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Option A: Conduction current density

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Option C: Polarization

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Option D: Magnetization

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