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# Finding the total charge on a semicircular disk

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Please see the attached file for full problem description
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.

https://brainmass.com/physics/applied-physics/finding-total-charge-semicircular-disk-591886

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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 attached file) cos (see attached file).
The area of the strip (considering it triangular) will be:
(see attached file)

Or: (see attached file)

Thus the charge on the strip element will be given by:
(see attached file)

Or: (see attached file)

Hence by integrating we get the charge on the disk as:
(see attached file)

Or: (see attached file)

Or : (see attached file)

Or: (see attached file)

Or: (see attached file)

As the charge distribution is symmetric about x axis (cos (see attached file) is positive in fourth quadrant) y component of E at all points on x axis will be zero.

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