Electricity: Electric Field, Potential, and Capacitance with Calculus
There are six problem sets on the topic of Electric Field, Potential, and Capacitance using Calculus. All problems are multi-part problems requiring an extensive analysis. The problems target your ability to use the concepts of electric field, electric potential, and electric capacitance to solve problems related to the interaction of charges that create electrical fields.
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Problem Set EVCC1: Sphere with Constant Charge Density
For a charged sphere, determine the electric field strength and the electric potential value at any point from the center of the sphere out to infinity using Gauss’s Law and Calculus. Includes 3 multi-part problems.
Problem Set EVCC2: Sphere with Differing Charge Density
For a charged sphere with varying charge density, determine the electric field strength and the electric potential value at any point from the center of the sphere out to infinity using Gauss’s Law and Calculus. Includes 3 multi-part problems.
Problem Set EVCC3: Flat Plate with Constant Charge Density
For a charged flat plate, determine the electric field strength at any point from the plate out to infinity using Gauss’s Law and Calculus. In the last problem also determine the capacitance of 2 parallel flat plates and the electric potential between them. Includes 4 multi-part problems.
Problem Set EVCC4: Charged Concentric Spherical Shells
For a set of oppositely charged concentric spherical shells, determine the electric field strength at a point between the shells using Gauss’s Law and Calculus. Determine the capacitance of the setup and the electric potential between the shells. Includes 3 multi-part problems.
Problem Set EVCC5: Cylinder with Constant Charge Density
For a charged cylinder, determine the electric field strength and the electric potential value at any point from the center of the sphere out to a distance of 100 times the cylinder radius using Gauss’s Law and Calculus. Includes 3 multi-part problems.
Problem Set EVCC6: Ring with Constant Charge Density
For a charged ring, determine the electric field strength and the electric potential value at positions along a perpendicular line to the plane of the ring from the center of the ring out to infinity using Calculus. Includes 4 multi-part problems.