8.6 Gauss’s Law

• What does the term \oint \vec{E} \cdot d\vec{A}</latex> in Gauss's Law represent?

  Electric flux through surface
• What is the significance of Gauss's Law in calculating electric fields?

  Relates flux to charge
• What does Gauss's Law relate the electric flux through a closed surface to?

  Total enclosed charge
• What is the formula for electric flux through a surface?

  \Phi_{E} = \int \vec{E} \cdot d\vec{A}</latex>
• If the electric field is parallel to the surface, the electric flux through that surface is zero.

  False
• The formula for electric flux is $\Phi_{E} =$$\int \vec{E} \cdot d\vec{A}$, where $\vec{E}$ is the electric field vector and $d\vec{A}$ is the small area element
• If the enclosed charge $Q_{enc}$ is zero, the electric flux through the surface is also zero
• What is the mathematical formulation of Gauss's Law in terms of electric flux and enclosed charge?

  $\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• When $Q_{enc} =$$0$, the electric flux through the surface is zero
• Match the geometry with its application of Gauss's Law:

  Sphere ↔️ Point charge

  Cylinder ↔️ Infinitely long charged cylinder

  Plane ↔️ Uniformly charged plane
• What is the direction of the electric field for an infinite, uniformly charged plane?

  Perpendicular to plane
• For an infinitely long, uniformly charged cylinder, the electric flux through a closed cylindrical surface is proportional to the charge per unit length.


  True
• In Gauss's Law, the term $\epsilon_{0}$ represents the permittivity of free space
• Gauss's Law can be used to simplify calculations of electric fields in symmetric charge distributions.

  True
• Gauss's Law states that the electric flux through a closed surface is proportional to the total electric charge enclosed by that surface.


  True
• Gauss's Law can be used to simplify the calculation of electric fields in certain symmetric charge distributions.


  True
• What does Gauss's Law state about the total electric flux through a closed surface?

  Proportional to enclosed charge
• Electric flux is defined as the integral of the electric field over the area of the surface
• Match the term with its definition:

  $\Phi_{E}$ ↔️ Electric flux

  $\vec{E}$ ↔️ Electric field vector

  $d\vec{A}$ ↔️ Small area element

  \epsilon_{0}</latex> ↔️ Permittivity of free space
• Match the variable with its definition and formula:

  $\Phi_{E}$ ↔️ Electric flux, $\int \vec{E} \cdot d\vec{A}$

  $\vec{E}$ ↔️ Electric field vector, Constant or variable in space

  $d\vec{A}$ ↔️ Small area element, Determined by surface geometry
• According to Gauss's Law, the electric flux through a closed surface is proportional to the total electric charge enclosed
• Why is Gauss's Law useful for calculating electric fields, especially for symmetric charge distributions?

  Simplifies flux calculations
• What is the significance of knowing $Q_{enc}$ in electric field calculations?


  Simplifies calculations
• For an infinitely long, uniformly charged cylinder, the electric field is radial and the flux through any closed cylindrical surface is proportional to the enclosed charge per unit length
• Match the geometry with its application of Gauss's Law:

  Sphere ↔️ Point charge

  Cylinder ↔️ Infinitely long charged cylinder

  Plane ↔️ Uniformly charged plane
• What is the mathematical expression for Gauss's Law?

  $\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• The permittivity of free space in Gauss's Law is denoted by the symbol $\epsilon_{0}$, which has a constant value
• In Gauss's Law, the term $\oint \vec{E} \cdot d\vec{A}$ represents the electric flux through the closed surface.
• In Gauss's Law, the term $Q_{enc}$ represents the total electric charge enclosed by the surface
• Electric flux measures the flow of the electric field through a given surface
• The SI unit for electric flux is $\text{N m}^{2} / \text{C}$, which stands for newton-meter squared per coulomb
• Gauss's Law states that the total electric flux through a closed surface is proportional to the enclosed charge.

  True
• Gauss's Law relates electric flux through a closed surface to the total charge enclosed by that surface.


  True
• Gauss's Law is useful for simplifying electric field calculations in symmetric charge distributions.

  True
• If the enclosed charge within a closed surface is zero, the electric flux through that surface is also zero.


  True
• If $Q_{enc} \neq 0$, the electric flux is proportional to the enclosed charge.


  True
• For a point charge, the electric field is radial and the flux through a closed spherical surface is proportional to the enclosed charge.


  True
• The electric field due to a point charge varies as $1 / r^{2}$.


  True
• What is the proportionality factor between the electric flux and the surface charge density for an infinite, uniformly charged plane?

  $\epsilon_{0}$