Provide a qualitative sketch of E(r). Make sure that all the important values of

Question

Provide a qualitative sketch of E(r). Make sure that all the important values of E are appropriately labeled. A non-conducting solid sphere of radius a is charged uniformly with charge density rho. Compute the electric potential a point P located at distance r from the center. Consider the two relevant regions: ra For each answer check the units. For the last region comment on the asymptotic behavior of V(r), as r rightarrow infinity. Provide a qualitative sketch of V(r). Make sure that all the important values of V are appropriately labeled. Two very long hollow coaxial cylinders of radii a and b (a

Explanation / Answer

when r>a
electric potential, = k*Q/r
where q = 4*a^3/3

hence , potential = k*4*a^3/3r

as r tends to infinity, potential will tend to zero

potential at the surface of sphere =  k*4*a^3/3a

=  k*4*a^2/3

now, no work is done from taking the charge from the surface to the inside of the sphere

hence, potential inside is constant abd eqaual to potential at the surface

so,

when r<a

potential = k*4*a^2/3

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