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Questions and Answers
What is electric flux?
What is electric flux?
The total number of electric field lines passing through the normal surface area.
The electric flux is directly proportional to the magnitude of charge.
The electric flux is directly proportional to the magnitude of charge.
True
What is the formula for electric flux?
What is the formula for electric flux?
Φ = EA cos θ
Match the following closed surfaces with their corresponding electric flux result (Φ):
Match the following closed surfaces with their corresponding electric flux result (Φ):
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What is the electric permittivity (ε0)?
What is the electric permittivity (ε0)?
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For a point charge of 1.8 µC at the center of a cubical Gaussian surface with edge length 55 cm, the net electric flux through the surface is ___ N·m²/C.
For a point charge of 1.8 µC at the center of a cubical Gaussian surface with edge length 55 cm, the net electric flux through the surface is ___ N·m²/C.
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In Gauss's law, what is the equation used to express the relationship between electric flux and charge?
In Gauss's law, what is the equation used to express the relationship between electric flux and charge?
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How is the electric field derived for a point charge using Gauss's law?
How is the electric field derived for a point charge using Gauss's law?
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What is the relationship between electric field (E) and charge per unit length (λ) for an infinite line of charges?
What is the relationship between electric field (E) and charge per unit length (λ) for an infinite line of charges?
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Study Notes
Gaussian Surface
- A symmetrical imaginary closed surface that surrounds the charge from all directions.
- The shape of the surface is dependent on the shape of the charge distribution.
- Its integral is represented by ∫ A d, where A is the area.
- This integral represents the area of the Gaussian surface.
- Relevant areas include:
- Surface area of a sphere: 4πr²
- Side area of a cylinder: 2πrh
- Area of a circle: πr²
Vector Area
- A vector with magnitude A (area) and direction outward and normal to the Gaussian surface.
Scalar Product
- Represented by A · B = A × B cosθ
- When θ = 0, A · B = AB
- When θ = π, A · B = -AB
- When θ = 90, A · B = 0
Electric Flux
- The total number of electric field lines passing through a normal surface area.
- Proportional to the magnitude of the charge.
- Formula: Φ = Q/ε₀ where Φ is the electric flux, Q is the charge, and ε₀ is the permeability of free space.
- Units: N.m²/C
- Formula with electric field: Φ = E · A = EA cosθ
- Where:
- A is a vector normal to the surface, with magnitude A and direction normal to the surface
- θ is the angle between E and A
Gauss's Law
- Formula: ∫ E · dA = Qin/ε₀
- Where:
- Φ is the electric flux
- Qin is the sum of electric charge within the Gaussian surface
- ε₀ = 8.85 × 10⁻¹² C²/Nm² is the permittivity of free space.
Coulomb's law from Gauss’s Law
- The electric field at a distance (r) from a point charge q can be calculated using Gauss's law.
- Charge is a point charge (q)
- The Gaussian surface chosen is a sphere of radius r.
- Resulting formula: E = kq/r² or E = 1/4πε₀ * q/r²
- Where k = 1/4πε₀ and is equal to 9 × 10⁹ Nm²/C²
Applying Gauss’s Law
- The electric field at a distance (r) from an infinite line of charges of constant charge per unit length λ can be calculated using Gauss's law.
- Charge is a linear charge (Qin = λl), where λ is the charge per unit length and l is the length of the line charge.
- The Gaussian surface chosen is a cylinder of radius r and length L.
- Resulting formula: E = λ/2πε₀r, which can be written as E = 2kλ/r.
Steps to solve Gauss' law problems
- Identify the shape of the charge distribution (point charge, charged sphere, charged line, charged cylinder, charged surface)
- Choose a Gaussian surface that encloses the charge distribution based on its shape.
- Apply Gauss's law.
- Calculate the electric field by isolating E and simplifying.
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Description
This quiz covers the concepts of Gaussian surfaces, vector areas, scalar products, and electric flux. Test your understanding of how these principles relate to charge distributions and calculate relevant areas for different geometrical shapes. Explore the mathematical relationships and applications of these fundamental physics topics.
