8.6 Gauss’s Law

• What is the definition of electric flux?

  Electric field through surface
• Electric flux is defined as the dot product of the electric field and the area
• The formula for electric flux is $\Phi_{E} =$$\int \vec{E} \cdot d\vec{A}$.
• What does $\Phi_{E}$ represent in the electric flux formula?


  Electric flux
• Electric flux is a key concept in Gauss's Law.
• What does Gauss's Law state about electric flux through a closed surface?

  Proportional to enclosed charge
• The mathematical expression for Gauss's Law is \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_{0}}</latex>.
• Match the charge distribution with its Gaussian surface:

  Point charge ↔️ Spherical surface

  Infinite line of charge ↔️ Cylindrical surface

  Infinite plane of charge ↔️ Plane perpendicular to surface
• What is the key to applying Gauss's Law to symmetrical charge distributions?

  Choosing a Gaussian surface
• For an infinite line of charge, the electric field is radially outward
• For an infinite plane of charge, the electric field is perpendicular to the surface.
• Match the charge distribution with its appropriate Gaussian surface:

  Point charge ↔️ Spherical surface

  Infinite line of charge ↔️ Cylindrical surface

  Infinite plane of charge ↔️ Plane perpendicular to the surface
• For a point charge, the electric field is radially outward
• For an infinite plane of charge, the electric field is perpendicular to the surface.
• What is electric flux defined as?

  Dot product of $\vec{E}$ and $d\vec{A}$
• Match the term with its definition:

  $\Phi_{E}$ ↔️ Electric flux

  $\vec{E}$ ↔️ Electric field

  $d\vec{A}$ ↔️ Infinitesimal area vector
• Gauss's Law states that the electric flux through any closed surface is proportional to the total charge enclosed by that surface.
• $\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$ is the mathematical expression of Gauss's
• Steps to apply Gauss's Law to symmetrical charge distributions:

  1️⃣ Choose an appropriate Gaussian surface

  2️⃣ Calculate the electric flux through the Gaussian surface

  3️⃣ Apply Gauss's Law to relate flux and charge

  4️⃣ Determine the electric field
• What type of charge distributions can Gauss's Law be used to calculate the electric field for?

  Symmetric
• Gauss's Law states that the electric flux through any closed surface is proportional to the total charge
• The mathematical expression for Gauss's Law is $\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• What does the term $\epsilon_{0}$ represent in Gauss's Law?


  Permittivity of free space
• Gauss's Law simplifies electric field calculations for symmetric charge distributions by using a Gaussian surface.
• For a point charge, the appropriate Gaussian surface is a spherical surface.
• What is the flux through a cylindrical Gaussian surface for an infinite line of charge?

  $\frac{\lambda}{2\pi\epsilon_{0}}$
• Match the charge distribution with its appropriate Gaussian surface:

  Point charge ↔️ Spherical surface

  Infinite line of charge ↔️ Cylindrical surface

  Infinite plane of charge ↔️ Plane perpendicular to the surface
• Gauss's Law and Coulomb's Law are both used to calculate electric fields but for different situations.
• What is the purpose of Gauss's Law?

  Electric field for symmetry
• Gauss's Law requires a closed Gaussian surface, whereas Coulomb's Law does not require a surface.
• Match the key feature with the correct law:

  Symmetry reliance ↔️ Gauss's Law

  Calculates force between point charges ↔️ Coulomb's Law