Consider a long, cylindrical charge distribution of radius R with a uniform charge density . Find the electric

Question

Consider a long, cylindrical charge distribution of radius R with a uniform charge density . Find the electric field at distance r from the axis, where r < R. (Use epsilon_0 for 0, rho for , and R and r as necessary.)
E =

Answer 1

The answer is:



(rho*r)/(2*epsilon_0)



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Answer 2

We can use a Gaussian surface inside the charge distribution, so surface int (E-dA) = Q/ epsilon_0. But, we have to solve for Q. Q in this case has to be solved through proportions. Since Q net = pi r^2 h rho (h is length), then Q inside is pi r^2 h rho. Also, E and da are perpendicular since the field lines radiate radially outward. Thus EA = Q/epsilon_0 -> E(2 pi r h) = ( pi r^2 h rho)/epsilon_0 -> E = rho / 2epsilon_0. We use h as a placeholder, and this cancels out so we get the final answer.

Answer 3

If the section at distance R is E0, then that is likewise E0 at 2R. the component of an infinite plane of value has an comparable value everywhere (?/2??). This top popular consequence of Gauss's regulation is defined in all subject-loose textual content fabric fabric books.