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Calculus: Solving Total Electric Flux with Integration

Learn how to find the total electric flux using calculus. Understand the concepts of substitution and limits of integration, with a focus on a quarter of a circle. Discover the definition of flux, substitution rules, and standard integration methods. Utilize the symmetry of a sphere to simplify calculations and evaluate the integral efficiently.

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Calculus: Solving Total Electric Flux with Integration

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  1. E-MAG Calculus Joseph Cantrell

  2. Total E is x components only Substitute dq to make it solvable Limits of integration: only ¼ of a circle

  3. Definition of Flux Substitution of “B” Substituting “dA” for “b dr” Limits: flux from d to d+a Standard integration Evaluation and “ln” properties Substitution of given “I” function

  4. Using symmetry of a sphere, the E-field due to any area dA is constant, so it can be removed from the integral. dA points to the normal of the sphere, so the angle between E and dA is 0 degrees. dA, when integrated, will be the surface area of the sphere

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