10.7 Electric Flux

• What is electric flux a measure of?

  Electric field through surface
• The formula for electric flux is \Phi_{E}
• The electric flux is zero when the surface is parallel to the electric field
• Electric flux is minimized when the surface is parallel to the electric field.


  True
• The formula for Gauss's Law is \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_{0}}.
• The formula for electric flux is \Phi_{E} = \int \vec{E} \cdot d\vec{A}
• Electric flux is used in Gauss's Law to relate the electric field to the charge enclosed within a closed surface.
• Electric flux is essential for calculating charge enclosed using Gauss's Law.

  True
• Match the variable with its meaning in Gauss's Law:

  \Phi_{E} ↔️ Electric flux

  \vec{E} ↔️ Electric field

  Q_{enc} ↔️ Enclosed charge
• 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}}$
• What is $d\vec{A}$ called in the context of electric flux calculations?


  Infinitesimal area vector
• What does $\Phi_{E}$ represent in the electric flux formula?


  Electric flux
• The electric flux is maximum when the surface is perpendicular to the electric field.


  True
• For a point charge at the center of a sphere, what is the shape of the Gaussian surface used to simplify the electric field calculation?

  Sphere
• For a spherical charge distribution, the electric field at a distance $r$ is $E =$$\frac{Q}{4\pi \epsilon_{0} r^{2}}$, assuming $r$ is greater than the radius
• The electric flux is maximized when the surface is parallel to the electric field.

  False
• Under what condition is the electric flux at its maximum value?

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

  Proportional to enclosed charge
• What is the first step in calculating electric flux using Gauss's Law?

  Choose a Gaussian surface
• Which surface orientation results in maximum electric flux through a Gaussian surface?

  Perpendicular to field
• What is the electric flux when the surface is perpendicular to the electric field?

  Maximum flux
• What are the three factors that electric flux depends on?

  Electric field strength, surface size, angle
• What does Gauss's Law state about electric flux through a closed surface?

  Proportional to enclosed charge
• The formula for Gauss's Law is \Phi_{E} = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_{0}}
• The permittivity of free space is denoted by \epsilon_{0}.
• The electric flux is zero when the surface is parallel to the electric field.


  True
• The electric flux formula is $\Phi_{E} =$$\int \vec{E} \cdot d\vec{A}$.


  True
• What does $d\vec{A}$ represent in the electric flux formula?


  Infinitesimal area vector
• Gauss's Law is expressed as $\oint \vec{E} \cdot d\vec{A} =$$\frac{Q_{enc}}{\epsilon_{0}}$, where \epsilon_{0}</latex> is the permittivity
• Steps to apply Gauss's Law for a spherical charge distribution

  1️⃣ Identify the symmetry of the charge distribution

  2️⃣ Choose a Gaussian surface concentric with the charge distribution

  3️⃣ Calculate the electric flux through the Gaussian surface

  4️⃣ Relate the flux to the enclosed charge using Gauss's Law

  5️⃣ Solve for the electric field
• What is the electric flux when the surface is perpendicular to the electric field?

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


  True
• What is electric flux a measure of?

  Electric field passing through surface
• Electric flux depends on the orientation of the surface relative to the electric field.


  True
• What is the differential area vector $d\vec{A}$ in Gauss's Law?


  Infinitesimal area element
• What is the formula to calculate electric flux directly?

  $\Phi_{E} =$$\int \vec{E} \cdot d\vec{A}$
• The electric flux depends on the orientation of the surface relative to the electric field
• In the electric flux formula, $\vec{E}$ represents the electric field
• What does Gauss's Law relate the electric flux through a closed surface to?

  Enclosed charge
• The electric field due to a point charge at a distance $r$ is given by $E =$$\frac{Q}{4\pi \epsilon_{0} r^{2}}$.


  True