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How to find surface integral of vector field in cylindrical coordinates through a...

Discussion in 'Mathematics' started by user3458571, Aug 1, 2020 at 8:03 PM.

  1. user3458571

    user3458571 Guest

    Trying to work through drill problem 3.9 from the 8th edition of the textbook "Engineering Electromagnetics by Hayt".

    this is the problem question:
    Given the field D = 6ρ sin(0.5φ) + 1.5ρ cos(0.5φ) C/m^2, evaluate both sides of the divergence theorem for the region bounded by ρ = 2, φ = 0, φ = π, z = 0, and z = 5.

    I am having trouble evaluating the surface integral side of the divergence theorem. My logic is that the surface integral is a sum of the surface integral through the half spherical section and the surface integral through the rectangular plane on the y = 0 axis.

    My main problem is trying to find the surface integral through the rectangular portion as I am not too sure how to go about it. any tips would be helpful!

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