Podcast
Questions and Answers
Electric flux is best described as being proportional to which quantity concerning electric field lines passing through a surface?
Electric flux is best described as being proportional to which quantity concerning electric field lines passing through a surface?
- The intensity of color of the lines.
- The average speed of the lines.
- The total length of the lines.
- The number of lines. (correct)
If a closed surface encloses a charge, what determines the net number of electric field lines passing through it?
If a closed surface encloses a charge, what determines the net number of electric field lines passing through it?
- The shape of the surface.
- The size of the enclosed charge. (correct)
- The material properties of the surface.
- The color of the surface.
When an electric field is uniform and oriented perpendicular to a rectangular surface of area A, how is the electric flux $Φ$ calculated?
When an electric field is uniform and oriented perpendicular to a rectangular surface of area A, how is the electric flux $Φ$ calculated?
- $Φ = E + A$
- $Φ = E/A$
- $Φ = EA$ (correct)
- $Φ = A/E$
If a surface with area A is oriented at an angle $\theta$ to a uniform electric field E, the electric flux through the surface is proportional to:
If a surface with area A is oriented at an angle $\theta$ to a uniform electric field E, the electric flux through the surface is proportional to:
When calculating electric flux through a non-uniform field incident on an irregular surface, what approach is used?
When calculating electric flux through a non-uniform field incident on an irregular surface, what approach is used?
How is the total electric flux ($\Phi$) through a surface calculated if the electric field ($\vec{E}$) is constant over small area elements ($d\vec{A}$)?
How is the total electric flux ($\Phi$) through a surface calculated if the electric field ($\vec{E}$) is constant over small area elements ($d\vec{A}$)?
For a closed surface, how do you determine the net electric flux?
For a closed surface, how do you determine the net electric flux?
Consider a sphere. If the electric field lines are entering the sphere are equal to the number of lines leaving it, what can be said about the net flux?
Consider a sphere. If the electric field lines are entering the sphere are equal to the number of lines leaving it, what can be said about the net flux?
According to Gauss's Law, what is the relationship between the net electric flux through a closed surface and the charge enclosed by that surface?
According to Gauss's Law, what is the relationship between the net electric flux through a closed surface and the charge enclosed by that surface?
Gauss's Law relates which of the following?
Gauss's Law relates which of the following?
If a charge q is located at the center of a sphere, the electric field at the surface of the sphere is proportional to which of the following?
If a charge q is located at the center of a sphere, the electric field at the surface of the sphere is proportional to which of the following?
If a closed spherical surface encloses a charge of q, how does the net electric flux change if the radius of the sphere is doubled?
If a closed spherical surface encloses a charge of q, how does the net electric flux change if the radius of the sphere is doubled?
A closed surface encloses a charge q. If the surface is changed from a sphere to a cube, what happens to the net electric flux through the surface?
A closed surface encloses a charge q. If the surface is changed from a sphere to a cube, what happens to the net electric flux through the surface?
A point charge is located outside a closed surface of arbitrary shape. What is the net electric flux through the surface?
A point charge is located outside a closed surface of arbitrary shape. What is the net electric flux through the surface?
What determines the electric field of a system with discrete charges or a continuous charge distribution?
What determines the electric field of a system with discrete charges or a continuous charge distribution?
If the net flux through a Gaussian surface is zero, which statement must be true?
If the net flux through a Gaussian surface is zero, which statement must be true?
A spherical Gaussian surface surrounds a point charge q. If the charge is tripled, what happens to the flux through the surface?
A spherical Gaussian surface surrounds a point charge q. If the charge is tripled, what happens to the flux through the surface?
How does the electric flux through a Gaussian surface change if the volume of the enclosed sphere is doubled while the charge remains constant?
How does the electric flux through a Gaussian surface change if the volume of the enclosed sphere is doubled while the charge remains constant?
If the surface enclosing a charge is changed from a sphere to a cube, how does the electric flux through the surface change?
If the surface enclosing a charge is changed from a sphere to a cube, how does the electric flux through the surface change?
A charge is moved to another location inside a Gaussian surface. How does this affect the electric flux through the surface?
A charge is moved to another location inside a Gaussian surface. How does this affect the electric flux through the surface?
What parameter is characterized using these terms: volume charge density, surface charge density and linear charge density?
What parameter is characterized using these terms: volume charge density, surface charge density and linear charge density?
If a charge Q is uniformly distributed over a volume V, how is the volume charge density ($\rho$) defined?
If a charge Q is uniformly distributed over a volume V, how is the volume charge density ($\rho$) defined?
The electric field due to a point charge can be calculated using Gauss's Law by selecting what?
The electric field due to a point charge can be calculated using Gauss's Law by selecting what?
When applying Gauss's Law to calculate the electric field due to a point charge, what geometrical relationship between the electric field and the Gaussian surface simplifies the calculation?
When applying Gauss's Law to calculate the electric field due to a point charge, what geometrical relationship between the electric field and the Gaussian surface simplifies the calculation?
For a uniformly charged sphere, how does the electric field outside the sphere compare to that of a point charge?
For a uniformly charged sphere, how does the electric field outside the sphere compare to that of a point charge?
Inside of a uniformly charged sphere, what happens to the electric field as the distance from the center increases?
Inside of a uniformly charged sphere, what happens to the electric field as the distance from the center increases?
If a thin spherical shell has a total charge Q distributed uniformly over its surface, what is the electric field inside the shell?
If a thin spherical shell has a total charge Q distributed uniformly over its surface, what is the electric field inside the shell?
Outside of a thin spherical shell with total charge $Q$ and radius R, what is the electric field a distance $r$ from the center?
Outside of a thin spherical shell with total charge $Q$ and radius R, what is the electric field a distance $r$ from the center?
What is the appropriate Gaussian surface to calculate the electric field at a distance r from a uniform positive line charge using Gauss's Law?
What is the appropriate Gaussian surface to calculate the electric field at a distance r from a uniform positive line charge using Gauss's Law?
Given a uniform positive line charge, how is the electric field oriented with respect to a cylindrical Gaussian surface used to calculate it?
Given a uniform positive line charge, how is the electric field oriented with respect to a cylindrical Gaussian surface used to calculate it?
How is a Gaussian surface constructed to determine the electric field due to a non-conducting, infinite plane of positive charge?
How is a Gaussian surface constructed to determine the electric field due to a non-conducting, infinite plane of positive charge?
For a cylinder-shaped Gaussian surface when finding the electric field due to a plane of charge, how is the electric field oriented?
For a cylinder-shaped Gaussian surface when finding the electric field due to a plane of charge, how is the electric field oriented?
What condition defines electrostatic equilibrium in a conductor?
What condition defines electrostatic equilibrium in a conductor?
What is the electric field at everywhere inside a conductor in electrostatic equilibrium?
What is the electric field at everywhere inside a conductor in electrostatic equilibrium?
Where does any net charge reside on an isolated conductor?
Where does any net charge reside on an isolated conductor?
What is the direction of the electric field just outside a charged conductor in electrostatic equilibrium?
What is the direction of the electric field just outside a charged conductor in electrostatic equilibrium?
On an irregularly shaped conductor, where does charge tend to accumulate?
On an irregularly shaped conductor, where does charge tend to accumulate?
According to Gauss's law relating to conductors, where is the field strongest?
According to Gauss's law relating to conductors, where is the field strongest?
In a conducting slab placed in an external electric field, what happens to free electrons?
In a conducting slab placed in an external electric field, what happens to free electrons?
In a conductor, a state will be reached when the internal electric field balances that of the external field. What is the implication of this balance?
In a conductor, a state will be reached when the internal electric field balances that of the external field. What is the implication of this balance?
Flashcards
Electric Flux (Φ)
Electric Flux (Φ)
A measure of the number of electric field lines passing through a surface.
Flux & Enclosed Charge
Flux & Enclosed Charge
The electric flux through a surface is proportional to the enclosed charge, regardless of the surface's shape.
Electric Flux (Uniform E)
Electric Flux (Uniform E)
In a uniform electric field (E) perpendicular to a rectangular surface of area (A), electric flux (Φ) equals EA.
Flux (Non-Perpendicular)
Flux (Non-Perpendicular)
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Electric Field (Irregular Surface)
Electric Field (Irregular Surface)
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Closed Surface
Closed Surface
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Net Flux (Closed Surface)
Net Flux (Closed Surface)
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Gauss's Law
Gauss's Law
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Surface Shape & Flux
Surface Shape & Flux
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Charge Location and Flux
Charge Location and Flux
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Net Electric Flux Formula
Net Electric Flux Formula
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Zero Net Flux Implication
Zero Net Flux Implication
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Volume Charge Density (ρ)
Volume Charge Density (ρ)
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Surface Charge Density (σ)
Surface Charge Density (σ)
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Linear Charge Density (λ)
Linear Charge Density (λ)
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Definition of conductors
Definition of conductors
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Electrostatic Equilibrium
Electrostatic Equilibrium
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Zero Electric Field
Zero Electric Field
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Charge Accumulation
Charge Accumulation
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Study Notes
Chapter 24: Gauss's Law
- Chapter introduces the concept of electric flux and its applications using Gauss's Law.
Electric Flux
- Described qualitatively using electric field lines.
Electric Flux (Φ)
- Represents the number of electric field lines penetrating a surface.
- Electric flux is proportional to the charge (q) as N ∝ q, where N is the number of electric field lines.
- When a surface encloses a charge, the net number of lines that pass through the surface is proportional to the net charge, regardless of the surface's shape, so Φ₁ = Φ₂ = Φ₃.
Calculation of Electric Flux
- For a uniform electric field (E) and a rectangular surface (A) where the electric field lines are perpendicular, the number of lines per unit area is proportional to E.
- The number of lines is proportional to EA, and the electric flux is defined as Φ = EA.
- The units for electric flux are [Φ] = [E][A] = N/C * m² = N*m²/C
- If the surface is not perpendicular to the field, the normal to the surface of area "A" makes an angle θ with the uniform field, the electric flux is Φ = E * A' = E * A cos θ.
- The flux can also be expressed as Φ = E • A.
- The number of lines crossing A equals the number of lines crossing the projected area A'.
- If the electric field is not uniform and the surface is irregular, the surface is divided into small elements, each with an area of ΔA.
- ΔA is a vector representing the area of the i-th element.
- It's assumed that the electric field Eᵢ is constant inside this small area element.
- The flux through the element is ΔΦᵢ = Eᵢ * ΔAᵢ cos θᵢ, or simply ΔΦᵢ = Eᵢ • ΔAᵢ.
- The total electric flux is given by Φ = Σ ΔΦᵢ = Σ Eᵢ • ΔAᵢ.
- For infinitesimally small elements, Φ = ∫Surface E • dA.
Electric Flux Through a Closed Surface
- A closed surface divides space into inside and outside regions.
- The net flux through the surface is given by Φc = ΦLeaving - ΦEntering, where Φc = § E • dA = § Eₙ dA.
- Eₙ = E cos θ, representing the normal component of E.
Example 24.1: Electric Flux Through a Sphere
- Find the electric flux through a sphere of radius 1.00 m with a charge of +1.00 μC at its center.
- The magnitude of the electric field is calculated, followed by use of the formula Φ = E • A.
- This gives Φ = EA = E(4πr²) = 9x10³(4π(1.0)²) = 1.13×10⁵ N•m²/C.
Gauss's Law
- This is used to solve this problem more easily.
Gauss’s Law
- Relates the net electric flux through a closed surface to the charge enclosed by the surface.
- For a positive charge q at the center of a sphere of radius r, the electric field at the surface is E = ke q/r².
- Φc = § E • dA = § E cos θdA
- Фс = § E dA, where En = E.
- The flux is Φc = § E dA, where A = 4πr² and E = keq/r², so Φc = 4πkeq.
- This formula means that the net electric flux through a closed spherical surface is proportional to the charge inside it.
- The net electric flux through a closed spherical surface is independent of its radius "r".
- This is because (E) is proportional to (1/r²) and (A) is proportional to (r²).
- Because of the shape of the surface, N1 = N2 = N3.
- The net flux is the same due to each surface, Φ1 = Φ2 = Φ3.
- This means Φc = q/ε₀ regardless of the surface shape.
Effect of Charge Location
- Electric charge located outside the surface.
Conceptual Example 24.3a
Answers with Gauss’s law to conceptual problems.
Properties of Conductors in Electrostatic Equilibrium
- Electric field is zero everywhere inside the conductor.
- Any charge on an isolated conductor resides on its surface.
- The electric field just outside a charged conductor is perpendicular to the surface and equals σ/ε₀, where σ is the charge per unit area.
- On an irregularly shaped conductor, charge accumulates at sharp locations.
Applications of Gauss’s Law
- Point charge
- Spherically symmetric charge distribution
- Outside the charged sphere
- Inside the charged sphere
- Thin spherical shell
- Outside the shell
- Inside the shell
- Cylindrically symmetric charge distribution.
- Non conducting infinite plane.
Charge Density
- When applying Gauss's Law, it's helpful to understand charge density concepts.
Volume Charge Density (ρ)
- If a charge Q is uniformly distributed over a volume V, the charge per unit volume is ρ = Q/V (C/m³).
Surface Charge Density (σ)
- Charge Q is uniformly distributed over a surface of area A, the charge per unit area is σ = Q/A (C/m²).
Linear Charge Density (λ)
- Charge Q is uniformly distributed over a line of length ℓ, the charge per unit length is λ = Q/ℓ (C/m).
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