Electric Flux - AP Physics C Electricity and Magnetism

1. If a surface is oriented parallel to $\boldsymbol{E}$, what is the flux through it?

   Electric flux is zero. Parallel means $\theta = 90°$, so $\cos\theta = 0$.

2. Find the electric flux: $\boldsymbol{E} = 10 \text{ N/C}$, $A = 1 \text{ m}^2$, $\theta = 45°$.

   Electric flux = $7.07 \text{ N m}^2/\text{C}$. Using $\Phi = 10 \times 1 \times \cos(45°) = 10 \times \frac{\sqrt{2}}{2} \approx 7.07$.

3. How does the electric flux through a closed surface change if its size is increased?

   Flux remains the same. Gauss's law depends only on enclosed charge.

4. What is the electric flux through a closed surface with no charge inside?

   Electric flux is zero. Gauss's law gives zero flux for zero enclosed charge.

5. How does electric flux change if the field direction is reversed?

   Electric flux changes sign. Reverses the dot product sign.

6. Calculate the flux for $\boldsymbol{E} = 12 \text{ N/C}$, $A = 3 \text{ m}^2$, $\theta = 0°$.

   Electric flux = $36 \text{ N m}^2/\text{C}$. Using $\Phi = 12 \times 3 \times \cos(0°) = 36$.

7. What happens to electric flux if the surface area is halved but orientation is unchanged?

   Flux is halved. Flux is directly proportional to area.

8. What is the value of electric flux if $Q_{\text{enc}} = 0$ inside a closed surface?

   Electric flux is zero. Gauss's law: flux equals enclosed charge divided by $\epsilon_0$.

9. What is the effect on flux if the angle between $\boldsymbol{E}$ and $\boldsymbol{A}$ changes from $0°$ to $90°$?

   Flux decreases to zero. Changing angle from maximum to zero flux.

10. Identify whether electric flux is scalar or vector.

    Electric flux is a scalar quantity. Has magnitude but no direction.

11. What is the relationship between electric flux and electric field strength?

    Flux is directly proportional to field strength. Linear relationship from flux formula.

12. Calculate flux for $\boldsymbol{E} = 9 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 60°$.

    Electric flux = $9 \text{ N m}^2/\text{C}$. Using $\Phi = 9 \times 2 \times \cos(60°) = 18 \times 0.5 = 9$.

13. What happens to electric flux if the area is doubled but field and angle remain constant?

    Electric flux doubles. Flux is directly proportional to area.

14. State the relationship between electric flux and charge enclosed for a closed surface.

    Flux is proportional to charge enclosed. Gauss's law states flux equals $Q_{enc}/\epsilon_0$.

15. Determine the electric flux if $\boldsymbol{E} = 0$ at the surface.

    Electric flux is zero. No field means no flux through any surface.

16. Find the electric flux through a closed surface: $Q_{\text{enc}} = 5 \text{ C}$.

    Electric flux = $\frac{5}{\boldsymbol{e_0}}$. Direct application of Gauss's law.

17. Find the electric flux: $\boldsymbol{E} = 6 \text{ N/C}$, $A = 4 \text{ m}^2$, $\theta = 90°$.

    Electric flux = $0 \text{ N m}^2/\text{C}$. At 90°, $\cos\theta = 0$, making flux zero.

18. Explain the effect on electric flux when the field is parallel to the surface.

    Flux is zero. Parallel field means $\theta = 90°$, so flux is zero.

19. State the condition for maximum electric flux through a given surface.

    When $\theta = 0°$. Field perpendicular to surface maximizes $\cos\theta$.

20. Calculate the flux for $\boldsymbol{E} = 4 \text{ N/C}$, $A = 3 \text{ m}^2$, $\theta = 60°$.

    Electric flux = $6 \text{ N m}^2/\text{C}$. Using $\Phi = 4 \times 3 \times \cos(60°) = 12 \times 0.5 = 6$.

21. Find the electric flux: $\boldsymbol{E} = 10 \text{ N/C}$, $A = 1 \text{ m}^2$, $\theta = 45^\circ$.

    Electric flux = $7.07 \text{ N m}^2/\text{C}$. Using $\Phi = 10 \times 1 \times \cos(45^\circ) = 10 \times \frac{\sqrt{2}}{2} \approx 7.07$.

22. What is the unit of electric flux in the International System of Units (SI)?

    The unit is $\text{N m}^2/\text{C}$. Derived from force per charge times area.

23. What is the electric flux through a cylindrical surface with no charge inside?

    Electric flux is zero. Gauss's law: no enclosed charge means zero flux.

24. What is the direction of the area vector $\boldsymbol{A}$ for a closed surface?

    Normal to the surface, pointing outward. Convention for closed surface orientation.

25. What is the formula for electric flux through a surface?

    $\text{Electric Flux} = \boldsymbol{E} \boldsymbol{\bullet} \boldsymbol{A} = EA\text{cos}\theta$. Dot product of electric field and area vector.

26. Find the electric flux: $\boldsymbol{E} = 5 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 0°$.

    Electric flux = $10 \text{ N m}^2/\text{C}$. Using $\Phi = EA\cos(0°) = 5 \times 2 \times 1 = 10$.

27. State the electric flux through a closed surface if the charge is outside the surface.

    Electric flux is zero. Gauss's law: flux depends only on enclosed charge.

28. What is the effect on electric flux if $\boldsymbol{E}$ is increased while $A$ and $\theta$ are constant?

    Electric flux increases. Flux is directly proportional to field strength.

29. What is the formula for calculating flux through an open surface?

    $\text{Electric Flux} = \int \boldsymbol{E} \cdot d\boldsymbol{A}$. General formula for any surface shape.

30. How is electric flux through a surface related to the electric field lines passing through it?

    It is proportional to the number of lines. Field lines represent flux density.

31. Find the electric flux through a surface: $\boldsymbol{E} = 15 \text{ N/C}$, $A = 2 \text{ m}^2$, $\theta = 0°$.

    Electric flux = $30 \text{ N m}^2/\text{C}$. Using $\Phi = 15 \times 2 \times \cos(0°) = 30$.

32. How is electric flux affected if the angle between $\boldsymbol{E}$ and $\boldsymbol{A}$ is 90°?

    Electric flux is zero. At 90°, $\cos\theta = 0$, making flux zero.

33. What is the effect on flux if the electric field is perpendicular to the surface?

    Flux is maximized. Perpendicular field gives $\cos(0°) = 1$.

Study these flashcards