Gauss' Law

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Table of Contents

• Gauss’ Law
  • Key Definitions
  • Electric Flux
    • \(\Phi_E=\int_S\vec E \cdot d\vec A=\int_S E\cos \theta\space dA\)
    • \(\vec A = A\vec n\)
  • Gauss’ Law
    • \(\Phi=\oint_S\vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}=\frac{1}{\epsilon_0}\int dq\)

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Gauss’ Law

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Key Definitions

Gauss’ Law - The electric flux through any closed surface is proportional to the enclosed

Electric Flux - the amount of passing through a surface

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Electric Flux

Given by:

\(\Phi_E=\int_S\vec E \cdot d\vec A=\int_S E\cos \theta\space dA\)

Such that, given the normal vector to the surface:

\(\vec A = A\vec n\)

and, $\theta$ is the angle between the electric field and the normal vector, $\vec n$, to the surface

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Gauss’ Law

Given by:

\(\Phi=\oint_S\vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}=\frac{1}{\epsilon_0}\int dq\)

where $Q_{enc}$ is the total enclosed by the surface $S$ We can find the total charge using