Podcast
Questions and Answers
What is electric flux primarily proportional to?
What is electric flux primarily proportional to?
- The number of electric field lines penetrating a surface. (correct)
- The surface area divided by the electric field strength.
- The electric charge density on the surface.
- The electric potential squared.
Under what condition is the electric flux through a surface at its maximum when the electric field is uniform?
Under what condition is the electric flux through a surface at its maximum when the electric field is uniform?
- When the surface is perpendicular to the electric field. (correct)
- When the surface is at a 45-degree angle to the electric field.
- When the electric field is zero.
- When the surface is parallel to the electric field.
How does the electric flux change if a surface's area is doubled while the electric field remains constant and perpendicular to the surface?
How does the electric flux change if a surface's area is doubled while the electric field remains constant and perpendicular to the surface?
- It quadruples.
- It doubles. (correct)
- It is halved.
- It remains the same.
What is the electric flux through a closed surface enclosing no charge?
What is the electric flux through a closed surface enclosing no charge?
In a region where the electric field is uniform, a flat surface of area A is rotated from a position where it is perpendicular to the field ($\theta = 0^\circ$) to a position where it is parallel to the field ($\theta = 90^\circ$). How does the electric flux through the surface change during this rotation?
In a region where the electric field is uniform, a flat surface of area A is rotated from a position where it is perpendicular to the field ($\theta = 0^\circ$) to a position where it is parallel to the field ($\theta = 90^\circ$). How does the electric flux through the surface change during this rotation?
If the net electric flux through a closed surface is positive, what can be concluded about the charge enclosed by the surface?
If the net electric flux through a closed surface is positive, what can be concluded about the charge enclosed by the surface?
A charge q is enclosed within a spherical Gaussian surface of radius r. If the radius of the Gaussian surface is doubled to 2_r_, how does the electric flux through the surface change?
A charge q is enclosed within a spherical Gaussian surface of radius r. If the radius of the Gaussian surface is doubled to 2_r_, how does the electric flux through the surface change?
Consider a cube placed in a uniform electric field. Under what conditions will the net electric flux through the cube be zero?
Consider a cube placed in a uniform electric field. Under what conditions will the net electric flux through the cube be zero?
What is the significance of $\oint \vec{E} \cdot d\vec{A}$ in the context of Gauss's Law?
What is the significance of $\oint \vec{E} \cdot d\vec{A}$ in the context of Gauss's Law?
A point charge q is located outside a closed surface. What is the net electric flux through the surface due to this charge?
A point charge q is located outside a closed surface. What is the net electric flux through the surface due to this charge?
Flashcards
Electric Flux (ΦE)
Electric Flux (ΦE)
The product of the electric field magnitude and the surface area perpendicular to the field. Measured in N·m²/C.
Electric Flux Formula (Uniform Field)
Electric Flux Formula (Uniform Field)
ΦE = EA cos θ. It's the electric flux through a surface, considering the angle θ between the electric field and the surface normal.
General Definition of Electric Flux
General Definition of Electric Flux
ΦE = ∫ E · dA. The integral of the electric field dotted with the area vector over a surface.
Closed Surface
Closed Surface
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Net Electric Flux (Closed Surface)
Net Electric Flux (Closed Surface)
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Gauss's Law
Gauss's Law
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Gaussian Surface
Gaussian Surface
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Study Notes
- Electric flux is the product of the magnitude of the electric field and the surface area perpendicular to the field.
- Electric flux is proportional to the number of electric field lines penetrating a surface.
- The units for electric flux are newton meters squared per coulomb (N⋅m²/C).
Non-Perpendicular Surfaces
- When a surface is not perpendicular to the electric field, the flux is less than EA.
- If the normal to the surface is at an angle θ to the electric field, then ΦE = EA cos θ.
- The flux is maximum (EA) when the surface is perpendicular to the field (θ = 0°).
- The flux is zero when the surface is parallel to the field (θ = 90°).
- E cos θ is the component of the electric field perpendicular to the surface and can be denoted as Eₙ.
Non-Uniform Electric Fields
- For non-uniform fields, the flux is defined for small area elements (ΔAᵢ).
- ΔAᵢ has a magnitude representing the area of the element, and a direction perpendicular to the surface element.
- The electric flux through the element is ΦEᵢ = Eᵢ ⋅ ΔAᵢ = EᵢΔAᵢ cos θᵢ.
- In this formula, θᵢ is the angle between the electric field Eᵢ and the vector ΔAᵢ.
- The total flux through the surface is approximated by summing the flux through all elements: ΦE ≈ Σ Eᵢ ⋅ ΔAᵢ.
General Definition of Electric Flux
- The general definition for electric flux is ΦE = ∫E ⋅ dA, integrated over the surface.
- Gauss's law states that the value of ΦE depends on the field pattern and the surface.
Closed Surfaces
- A closed surface divides space into inside and outside regions.
- For a closed surface, the area vector points outward from the surface.
- The net flux through a closed surface is ∫EdA .
- This is proportional to the net number of lines leaving the surface.
- Positive flux means more lines are leaving than entering and negative flux means more lines are entering than leaving.
- The flux is zero when the field lines graze the surface and are tangential to it.
Gauss's Law
- Gauss's Law relates the net electric flux through a closed surface (gaussian surface) and the charge enclosed by the surface
- The net flux through any closed surface surrounding a point charge q is given by q/ε₀, and is independent of the shape of that surface
- Gauss’s law states: ΦE = q/ε₀
- This is used to calculate the electric flux through a cube with uniform electric field, in this case giving a net electric flux of zero
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