3. Consider three uniform charge distributions: (1) a uniformly charged pyramid,

Question

3. Consider three uniform charge distributions: (1) a uniformly charged pyramid, (2) a uniformly charged sphere, and (3) a uniformly charged cylinder with finite length, a. Which of these systems possess continuous symmetries? For those that do, how many distinct continuous symmetries does the charge distribution have? b. For which of these systems could you use Gauss’ law to find the electric field? Explain. c. Consider a sphere with a non-uniform charge density: plP) = c". Could you use Gauss' law to find the electric field outside the sphere? Explain your reasoning. d. Generalize your results. To use Gauss’ law to find the electric field of a charge distribution, must it possess continuous symmetries? If so, what is the minimum number required?

Explanation / Answer

(a) Sphere and cylinder have continuous symmetry while pyramidal does not have continuous symmetry

(b) We can use gausaa law for both sphere and cylinder

(c)As figure is symmetrical we can use gauss law to find electric field but we need the integrate E.dA properly and also q/epsilon .

(d) To use gausaa law for finding electric field,we must choose a gaussian surface and this gaussian surface must be a closed surface with continuous symmetry such that we can choose infinite gaussian surfaca following the same symmetry

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