Electric flux density is a function of_______

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Examoogle · Accepted Answer

Charge

Explanation: Electric flux density ($\vec{D}$) is a vector field defined primarily by the charge distribution that produces the electric field. It represents the density of the electric displacement flux emanating from a charge, independent of the medium.

Working Principle: According to Gauss's Law, the total electric flux passing through a closed surface is equal to the total charge enclosed by that surface. Mathematically, the electric flux density is related to the charge density ($ho_v$) by the divergence theorem: $
abla \cdot \vec{D} = ho_v$. Because $\vec{D} = \epsilon_0\vec{E} + \vec{P}$, the density essentially quantifies the effect of free charges within a dielectric medium.

Key Formulas: $\vec{D} = \epsilon \vec{E}$ — Relation between flux density, permittivity, and electric field; $\oint_S \vec{D} \cdot d\vec{S} = Q_{enclosed}$ — Gauss's Law in integral form

Key Points: Electric flux density ($Δ$) is measured in Coulombs per square meter ($C/m^2$).; It is independent of the dielectric constant of the medium in terms of source charge.; The lines of flux density originate from positive charges and terminate on negative charges.

Advantages: Simplifies calculations in dielectric media.; Provides a direct link between free charge and electric field displacement.

Disadvantages: Does not account for induced polarization charges directly in the simplified $\vec{D}$ vector definition without the permittivity factor.; Can be complex to calculate for irregular geometries.

Applications: Capacitor design and dielectric constant analysis.; Electromagnetic boundary value problems.

Additional Info: The unit for Electric Flux Density is $C/m^2$.. Option A, C, and D are incorrect because while they relate to electrical parameters (volume charge density, current density, or potential difference), the fundamental source defined by the flux density vector field at any point in space is the free charge density.

Answer: B is correct — Electric flux density is fundamentally defined by the electric charge that creates the field.

Exam Tip: Remember that Electric Flux Density ($Δ$) relates to free charge, whereas Electric Field Intensity ($E$) depends on the medium properties through polarization.

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