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Math Help - nonuniformly charged spherical surface

  1. #1
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    nonuniformly charged spherical surface

    A sphere of radius a in free space is nonuniformly charged over its surface such that the charge density is given by ρs(θ) = ρs0 sin 2θ, where ρs0 is a constant and 0≤θ≤∏. Compute the total charge of the sphere.

    So I know
    ρs = dQ/dS

    Integrating the surface charge density function will give me the charge Q. My question is how would you set up this integral?

    ∫ρs0 sin 2θ dS
    integrating 0 to ∏

    Or would this involve much more than that such as a triple integral?

    Any help getting this set up would be great! Thanks!
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  2. #2
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    Re: nonuniformly charged spherical surface

    Since you are integrating over the surface, you should have a double integral. If you use spherical coordinates, one angle goes from 0 to 2\pi, the other goes from 0 to \pi, all the while the radius is constant.

    The surface element for a constant radius is

    dS = r^2 \sin \theta d\theta d\phi

    Can you set up the integral now?
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  3. #3
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    Re: nonuniformly charged spherical surface

    Yes after integration I got the total charge Q=0 C.

    Thanks for the help.
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