Consider an infinite slab of non-uniform symmetric volume charge density: rho(v)

Question

Consider an infinite slab of non-uniform symmetric volume charge density:

rho(v)=rho(v0)*|X|/d (-d/2<x<d/2).Find the electric field everywhere.Since the distribution is even
about x=0,it is expected that the electric field is antisymmetric.

Explanation / Answer

For rE*4pi*eps*r^2 = integration(0 to r) [rho_o*r^2*4pi*r^2*dr] => E*eps*r^2 = rho_o*{integration (0 to r) [r^4*dr]} => E*eps*r^2 = rho_o*r^5/5 => E = rho_o*r^3/(5*eps) --Answer Here, eps = absolute permittivity For r = a, in the above derived equation put r = a => E = rho_o*a^3/(5*eps) --Answer For r > a E*4pi*eps*r^2 = integration(0 to a) [rho_o*r^2*4pi*r^2*dr] => E*eps*r^2 = rho_o*a^5/5 => E = rho_o*a^5/(5*eps*r^2) --Answer

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