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Define linear charge density (λ).

Charge per unit length: λ = Q/L.

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Define linear charge density (λ).
Charge per unit length: λ = Q/L.
Define area charge density (σ).
Charge per unit area: σ = Q/A.
Define electric potential difference (ΔV).
The negative line integral of the electric field: $$ΔV = -\int E \cdot dl$$
Define *dq* in the context of extended charge distributions.
An infinitesimally small amount of charge, used when integrating over a continuous charge distribution.
Define Gaussian surface.
An imaginary closed surface used in conjunction with Gauss's Law to calculate the electric field.
What is Gauss' Law?
The total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity: $$\oint E \cdot dA = \frac{Q_{enc}}{ε_0}$$
Label the diagram of the Gaussian surface enclosing a line of charge.
1: Line of charge, 2: Cylindrical Gaussian surface, 3: Radius (r), 4: Length (L)
Label the diagram of the Gaussian surface enclosing a sphere.
1: Sphere of charge, 2: Spherical Gaussian surface, 3: Radius (r)
Label the diagram of the Gaussian surface enclosing an insulating sheet of charge.
1: Insulating sheet, 2: Rectangular Gaussian surface, 3: Area (A)
What are the general steps to calculate the electric field due to an extended charge distribution?
1. Break the total charge Q into tiny pieces dq. 2. Find the electric field dE due to each piece. 3. Integrate dE to find the total electric field E.
List the steps to apply Gauss' Law.
1. Choose a Gaussian surface. 2. Calculate the electric flux through the Gaussian surface. 3. Calculate the enclosed charge. 4. Apply Gauss' Law: $$\oint E \cdot dA = \frac{Q_{enc}}{ε_0}$$
How do you find the potential difference?
1. Use Gauss' Law to find an expression for E. 2. Plug that into: $$ΔV = -\int E \cdot dl$$
What is the process for calculating the electric field of a ring of charge at a point on its axis?
1. Express dq in terms of λ and dl. 2. Find dE using $$dE = k \frac{dq}{r^2}$$. 3. Integrate dE to find the total electric field E.
What is the process for calculating the electric field of a line of charge?
1. Express dq in terms of dy using the linear charge density λ. 2. Use the Pythagorean theorem to find r. 3. Integrate to find the total electric field.