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Finding the total charge on a semicircular disk

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6. You have a flat, semi-circular (half) disk of radius a in the x-y plane. (Like a DVD that has been chopped in half)

It has a nonuniform charge density (sigma = sigma0cos(phi) (where phi is the usual azimuthal angle in the x-y plane, as shown, and sigma0 > 0)

i) Compute the total charge on this disk (in terms of givens: a and sigma0)

ii) Consider the point (shown) on the +x axis (a given distance x0 from the origin). Do any components of the field E(x0,0, 0) at this points vanish "by inspection"? Explain.

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This solution discusses the total charge on a semicircular disk with charge density varying with azimuthal angle.

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Please see the attached file for full problem solution
Solution:
Consider an infinitely thin radial strip between angle (see attached file). The charge density on this strip can be considered as (see ...

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