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Continuous Charge Distribution

Define linear, surface, and volume charge densities and map them to integration concepts.

4 lessons

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Continuous Charge Density

Defines linear, surface, and volume densities.

When dealing with macroscopic objects like wires or metal plates, counting billions of discrete electrons is impractical. Instead, we treat the charge as a continuous fluid spreading uniformly over the object's geometry.

This "smoothed out" macroscopic average is defined as a charge density.

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Charge Distributions

Visual of line, surface, and volume charge segments.

Click to zoom

Charge can be continuously distributed along a line, over a surface, or throughout a volume.

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Densities Overview

Matrix comparing the three densities.

Linear Charge Density

λ

Definition:

λ = \frac{Δ Q}{Δ l}

Unit:

C m^{- 1}

Dimension:

[L^{- 1} T A]

Surface Charge Density

σ

Definition:

σ = \frac{Δ Q}{Δ S}

Unit:

C m^{- 2}

Dimension:

[L^{- 2} T A]

Volume Charge Density

ρ

Definition:

ρ = \frac{Δ Q}{Δ V}

Unit:

C m^{- 3}

Dimension:

[L^{- 3} T A]

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quiz

Selecting the Right Density

MCQ testing recognition of density application.

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Which charge density is most appropriate to describe the macroscopic charge distribution on a thin spherical shell?