10.7 Electric Flux

• The electric flux is maximized when the surface is parallel to the electric field.

  False
• Arrange the surface orientations in increasing order of electric flux.

  1️⃣ Parallel to field

  2️⃣ Angled to field

  3️⃣ Perpendicular to field
• What does \(Q_{enc}\) represent in Gauss's Law?

  Enclosed charge
• The formula for electric flux is $\oint \vec{E} \cdot d\vec{A}$
• Electric flux is a measure of the amount of electric field that passes through a given surface.


  True
• The electric flux depends on the orientation of the surface relative to the electric field.


  True
• The formula for Gauss's Law is $\Phi_{E} =$$\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• What does $\epsilon_{0}$ represent in Gauss's Law?


  Permittivity of free space
• What does electric flux measure?

  Electric field through a surface
• What is the electric flux when the surface is perpendicular to the electric field?

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


  True
• If no charge is enclosed within a Gaussian surface, the electric flux through it is zero.


  True
• The permittivity of free space is denoted by $\epsilon_{0}$.


  True
• What is the general formula for electric flux?

  $\Phi_{E} =$$\int \vec{E} \cdot d\vec{A}$
• Gauss's Law relates electric flux to the charge enclosed within a closed surface.


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

  True
• The formula to calculate electric flux is $\Phi_{E} =$$\int \vec{E} \cdot d\vec{A}$
• What does $\vec{E}$ represent in the electric flux formula?


  Electric field vector
• What is the formula for Gauss's Law?

  $\Phi_{E} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• The formula for electric flux is \Phi_{E} = $\int \vec{E} \cdot d\vec{A}$
• The electric flux is zero when the surface is parallel to the electric field.
• The formula for Gauss's Law is \oint \vec{E} \cdot d\vec{A}</latex> = $\frac{Q_{enc}}{\epsilon_{0}}$.
• Steps to calculate electric flux using Gauss's Law.

  1️⃣ Choose a closed Gaussian surface

  2️⃣ Calculate the total charge enclosed

  3️⃣ Apply the formula $\Phi_{E} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• If no charge is enclosed, the electric flux is zero
• In the electric flux formula, $d\vec{A}$ represents the infinitesimal area vector
• In a closed spherical surface around a point charge, what is the relationship between electric flux and charge?

  Directly proportional
• In Gauss's Law, $Q_{enc}$ represents the enclosed charge
• In the electric flux calculation formula, \vec{E}</latex> represents the electric field vector.

  True
• $d\vec{A}$ is the infinitesimal area vector.


  True
• $\epsilon_{0}$ is the permittivity of free space.


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

  Proportional to charge enclosed
• Match the concepts with their corresponding variables:

  Electric Flux ↔️ $\Phi_{E}$

  Electric Field ↔️ $\vec{E}$

  Infinitesimal Area ↔️ $d\vec{A}$
• What is the first step in using Gauss's Law to find the electric field of a charge distribution?

  Choose a closed Gaussian surface
• Gauss's Law is most effective for symmetric charge distributions because the electric field can be simplified using symmetry.


  True
• Steps to calculate electric flux using Gauss's Law:

  1️⃣ Identify the charge enclosed within the closed surface

  2️⃣ Plug the charge and permittivity values into the Gauss's Law formula

  3️⃣ Calculate the electric flux
• What is the electric flux through a surface enclosing a charge of 10 C, given $\epsilon_{0} =$$8.85 \times 10^{ - 12} \, \text{F / m}$?


  $1.13 \times 10^{12} \, \text{N m}^{2} / \text{C}$
• What is the formula for Gauss's Law when written in integral form?

  $\Phi_{E} =$$\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$
• The formula to calculate electric flux is $\Phi_{E}$
• According to Gauss's Law, the electric flux through a closed surface is directly proportional to the charge enclosed
• To calculate electric flux using Gauss's Law, you must first identify the charge enclosed within the closed surface.

  True