Electric Flux - AP Physics C: Electricity and Magnetism
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How is electric flux through a surface related to the electric field lines passing through it?
How is electric flux through a surface related to the electric field lines passing through it?
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It is proportional to the number of lines. Field lines represent flux density.
It is proportional to the number of lines. Field lines represent flux density.
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How is electric flux affected if the angle between $\boldsymbol{E}$ and $\boldsymbol{A}$ is 90°?
How is electric flux affected if the angle between $\boldsymbol{E}$ and $\boldsymbol{A}$ is 90°?
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Electric flux is zero. At 90°, $\cos\theta = 0$, making flux zero.
Electric flux is zero. At 90°, $\cos\theta = 0$, making flux zero.
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What happens to electric flux if the area is doubled but field and angle remain constant?
What happens to electric flux if the area is doubled but field and angle remain constant?
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Electric flux doubles. Flux is directly proportional to area.
Electric flux doubles. Flux is directly proportional to area.
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Identify whether electric flux is scalar or vector.
Identify whether electric flux is scalar or vector.
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Electric flux is a scalar quantity. Has magnitude but no direction.
Electric flux is a scalar quantity. Has magnitude but no direction.
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What is the effect on flux if the angle between $\boldsymbol{E}$ and $\boldsymbol{A}$ changes from $0°$ to $90°$?
What is the effect on flux if the angle between $\boldsymbol{E}$ and $\boldsymbol{A}$ changes from $0°$ to $90°$?
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Flux decreases to zero. Changing angle from maximum to zero flux.
Flux decreases to zero. Changing angle from maximum to zero flux.
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Find the electric flux through a surface: $\boldsymbol{E} = 15 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 0°$.
Find the electric flux through a surface: $\boldsymbol{E} = 15 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 0°$.
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Electric flux = $30 \text{ N m}^2/\text{C}$. Using $\Phi = 15 \times 2 \times \cos(0°) = 30$.
Electric flux = $30 \text{ N m}^2/\text{C}$. Using $\Phi = 15 \times 2 \times \cos(0°) = 30$.
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What is the effect on flux if the electric field is perpendicular to the surface?
What is the effect on flux if the electric field is perpendicular to the surface?
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Flux is maximized. Perpendicular field gives $\cos(0°) = 1$.
Flux is maximized. Perpendicular field gives $\cos(0°) = 1$.
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Find the electric flux through a closed surface: $Q_{\text{enc}} = 5 \text{ C}$.
Find the electric flux through a closed surface: $Q_{\text{enc}} = 5 \text{ C}$.
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Electric flux = $\frac{5}{\boldsymbol{e_0}}$. Direct application of Gauss's law.
Electric flux = $\frac{5}{\boldsymbol{e_0}}$. Direct application of Gauss's law.
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What is the electric flux through a cylindrical surface with no charge inside?
What is the electric flux through a cylindrical surface with no charge inside?
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Electric flux is zero. Gauss's law: no enclosed charge means zero flux.
Electric flux is zero. Gauss's law: no enclosed charge means zero flux.
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State the condition for maximum electric flux through a given surface.
State the condition for maximum electric flux through a given surface.
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When $\theta = 0°$. Field perpendicular to surface maximizes $\cos\theta$.
When $\theta = 0°$. Field perpendicular to surface maximizes $\cos\theta$.
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What is the value of electric flux if $Q_{\text{enc}} = 0$ inside a closed surface?
What is the value of electric flux if $Q_{\text{enc}} = 0$ inside a closed surface?
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Electric flux is zero. Gauss's law: flux equals enclosed charge divided by $\epsilon_0$.
Electric flux is zero. Gauss's law: flux equals enclosed charge divided by $\epsilon_0$.
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Find the electric flux: $\boldsymbol{E} = 6 \text{ N/C}$, $A = 4 \text{ m}^2$, $\theta = 90°$.
Find the electric flux: $\boldsymbol{E} = 6 \text{ N/C}$, $A = 4 \text{ m}^2$, $\theta = 90°$.
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Electric flux = $0 \text{ N m}^2/\text{C}$. At 90°, $\cos\theta = 0$, making flux zero.
Electric flux = $0 \text{ N m}^2/\text{C}$. At 90°, $\cos\theta = 0$, making flux zero.
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Find the electric flux: $\boldsymbol{E} = 10 \text{ N/C}$, $A = 1 \text{ m}^2$, $\theta = 45^\circ$.
Find the electric flux: $\boldsymbol{E} = 10 \text{ N/C}$, $A = 1 \text{ m}^2$, $\theta = 45^\circ$.
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Electric flux = $7.07 \text{ N m}^2/\text{C}$. Using $\Phi = 10 \times 1 \times \cos(45^\circ) = 10 \times \frac{\sqrt{2}}{2} \approx 7.07$.
Electric flux = $7.07 \text{ N m}^2/\text{C}$. Using $\Phi = 10 \times 1 \times \cos(45^\circ) = 10 \times \frac{\sqrt{2}}{2} \approx 7.07$.
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What is the relationship between electric flux and electric field strength?
What is the relationship between electric flux and electric field strength?
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Flux is directly proportional to field strength. Linear relationship from flux formula.
Flux is directly proportional to field strength. Linear relationship from flux formula.
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Calculate flux for $\boldsymbol{E} = 9 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 60°$.
Calculate flux for $\boldsymbol{E} = 9 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 60°$.
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Electric flux = $9 \text{ N m}^2/\text{C}$. Using $\Phi = 9 \times 2 \times \cos(60°) = 18 \times 0.5 = 9$.
Electric flux = $9 \text{ N m}^2/\text{C}$. Using $\Phi = 9 \times 2 \times \cos(60°) = 18 \times 0.5 = 9$.
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What is the unit of electric flux in the International System of Units (SI)?
What is the unit of electric flux in the International System of Units (SI)?
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The unit is $\text{N m}^2/\text{C}$. Derived from force per charge times area.
The unit is $\text{N m}^2/\text{C}$. Derived from force per charge times area.
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What is the effect on electric flux if $\boldsymbol{E}$ is increased while $A$ and $\theta$ are constant?
What is the effect on electric flux if $\boldsymbol{E}$ is increased while $A$ and $\theta$ are constant?
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Electric flux increases. Flux is directly proportional to field strength.
Electric flux increases. Flux is directly proportional to field strength.
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Calculate the flux for $\boldsymbol{E} = 12 \text{ N/C}$, $A = 3 \text{ m}^2$, $\theta = 0°$.
Calculate the flux for $\boldsymbol{E} = 12 \text{ N/C}$, $A = 3 \text{ m}^2$, $\theta = 0°$.
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Electric flux = $36 \text{ N m}^2/\text{C}$. Using $\Phi = 12 \times 3 \times \cos(0°) = 36$.
Electric flux = $36 \text{ N m}^2/\text{C}$. Using $\Phi = 12 \times 3 \times \cos(0°) = 36$.
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State the relationship between electric flux and charge enclosed for a closed surface.
State the relationship between electric flux and charge enclosed for a closed surface.
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Flux is proportional to charge enclosed. Gauss's law states flux equals $Q_{enc}/\epsilon_0$.
Flux is proportional to charge enclosed. Gauss's law states flux equals $Q_{enc}/\epsilon_0$.
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Determine the electric flux if $\boldsymbol{E} = 0$ at the surface.
Determine the electric flux if $\boldsymbol{E} = 0$ at the surface.
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Electric flux is zero. No field means no flux through any surface.
Electric flux is zero. No field means no flux through any surface.
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Calculate the flux for $\boldsymbol{E} = 4 \text{ N/C}$, $A = 3 \text{ m}^2$, $\theta = 60°$.
Calculate the flux for $\boldsymbol{E} = 4 \text{ N/C}$, $A = 3 \text{ m}^2$, $\theta = 60°$.
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Electric flux = $6 \text{ N m}^2/\text{C}$. Using $\Phi = 4 \times 3 \times \cos(60°) = 12 \times 0.5 = 6$.
Electric flux = $6 \text{ N m}^2/\text{C}$. Using $\Phi = 4 \times 3 \times \cos(60°) = 12 \times 0.5 = 6$.
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What is the direction of the area vector $\boldsymbol{A}$ for a closed surface?
What is the direction of the area vector $\boldsymbol{A}$ for a closed surface?
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Normal to the surface, pointing outward. Convention for closed surface orientation.
Normal to the surface, pointing outward. Convention for closed surface orientation.
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What is the electric flux through a closed surface with no charge inside?
What is the electric flux through a closed surface with no charge inside?
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Electric flux is zero. Gauss's law gives zero flux for zero enclosed charge.
Electric flux is zero. Gauss's law gives zero flux for zero enclosed charge.
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How does the electric flux through a closed surface change if its size is increased?
How does the electric flux through a closed surface change if its size is increased?
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Flux remains the same. Gauss's law depends only on enclosed charge.
Flux remains the same. Gauss's law depends only on enclosed charge.
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If a surface is oriented parallel to $\boldsymbol{E}$, what is the flux through it?
If a surface is oriented parallel to $\boldsymbol{E}$, what is the flux through it?
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Electric flux is zero. Parallel means $\theta = 90°$, so $\cos\theta = 0$.
Electric flux is zero. Parallel means $\theta = 90°$, so $\cos\theta = 0$.
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How does electric flux change if the field direction is reversed?
How does electric flux change if the field direction is reversed?
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Electric flux changes sign. Reverses the dot product sign.
Electric flux changes sign. Reverses the dot product sign.
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Find the electric flux: $\boldsymbol{E} = 5 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 0°$.
Find the electric flux: $\boldsymbol{E} = 5 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 0°$.
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Electric flux = $10 \text{ N m}^2/\text{C}$. Using $\Phi = EA\cos(0°) = 5 \times 2 \times 1 = 10$.
Electric flux = $10 \text{ N m}^2/\text{C}$. Using $\Phi = EA\cos(0°) = 5 \times 2 \times 1 = 10$.
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Identify whether electric flux is scalar or vector.
Identify whether electric flux is scalar or vector.
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Electric flux is a scalar quantity. Has magnitude but no direction.
Electric flux is a scalar quantity. Has magnitude but no direction.
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What is the formula for electric flux through a surface?
What is the formula for electric flux through a surface?
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$\text{Electric Flux} = \boldsymbol{E} \boldsymbol{\bullet} \boldsymbol{A} = EA\text{cos}\theta$. Dot product of electric field and area vector.
$\text{Electric Flux} = \boldsymbol{E} \boldsymbol{\bullet} \boldsymbol{A} = EA\text{cos}\theta$. Dot product of electric field and area vector.
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What is the formula for calculating flux through an open surface?
What is the formula for calculating flux through an open surface?
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$\text{Electric Flux} = \int \boldsymbol{E} \cdot d\boldsymbol{A}$. General formula for any surface shape.
$\text{Electric Flux} = \int \boldsymbol{E} \cdot d\boldsymbol{A}$. General formula for any surface shape.
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