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Steps to apply Gauss's Law?
1. Choose a Gaussian surface. 2. Calculate the electric flux through the surface. 3. Determine the enclosed charge. 4. Apply Gauss's Law: \(\Phi_E = \frac{Q_{enc}}{\epsilon_0}\).
Steps to calculate electric flux when \(E\) is uniform and perpendicular to \(A\)?
1. Identify the electric field \(E\). 2. Identify the area \(A\). 3. Calculate \(\Phi = EA\).
Steps to calculate electric flux when \(E\) is at an angle \(\theta\) to \(A\)?
1. Identify the electric field \(E\). 2. Identify the area \(A\). 3. Identify the angle \(\theta\) between \(E\) and \(A\). 4. Calculate \(\Phi = \vec{E} \cdot \vec{A} = EA \cos(\theta)\).
Steps to determine electric field for spherical symmetry using Gauss's Law?
1. Choose a spherical Gaussian surface. 2. Calculate the flux: \(\Phi = E(4\pi r^2)\). 3. Determine the enclosed charge \(Q_{enc}\). 4. Apply Gauss's Law to find \(E\).
Steps to find enclosed charge with non-uniform charge density \(\rho(r)\)?
1. Define the volume element \(dV\). 2. Set up the integral: \(q_{enc} = \int \rho(r) dV\). 3. Evaluate the integral to find \(q_{enc}\).
Difference between uniform and non-uniform charge density?
Uniform: Charge evenly distributed. | Non-uniform: Charge density varies with position.
Difference between flux entering and exiting a closed surface?
Entering: Negative flux. | Exiting: Positive flux.
Differences between conductors and insulators regarding electric fields?
Conductors: Electric field inside is zero. | Insulators: Electric field can exist inside.
Differences between electric flux and electric field?
Electric flux: Measure of field lines through an area. | Electric field: Force per unit charge at a point.
Differences between using Gauss's Law with spherical vs. cylindrical symmetry?
Spherical: Use spherical Gaussian surface, $A = 4\pi r^2$. | Cylindrical: Use cylindrical Gaussian surface, $A = 2\pi r L$.
What is electric flux?
The measure of how much of an electric field passes through a given area.
Define Gauss's Law.
The electric flux through a closed surface is proportional to the enclosed charge.
What is a Gaussian surface?
An imaginary closed surface used to apply Gauss's Law, chosen to simplify the calculation of electric flux.
What is \(\epsilon_0\)?
The permittivity of free space, a physical constant.
Define uniform charge density.
A charge distribution where the charge is evenly distributed throughout a volume or surface.
Define non-uniform charge density.
A charge distribution where the charge density varies with position.