# Gradient, potential and electric field

by brad sue
Tags: electric, field, gradient, potential
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 P: 284 Hi , I need help about procedure on this problem: Consider a sphere of charge density ρv= 2/r[C/m3] having a radius a (no charge outside), centered at the origin. Perform the following steps: a) Calculate the electric field both inside and outside the sphere using Gauss’ law. b) Calculate the potential inside and outside the sphere by integrating the electric field to get the potential, assuming zero Volts at infinity. c) Calculate the potential assuming that the reference is at the origin zero, V(0,0,0) =0 d) Find the electric field inside and outside the sphere by taking the gradient of the potential. You should be able to verify that your answer is the same as the electric field that you started with from Gauss’s law. I found the first question: for r E=1/ε0 for r>a--> E=a^2/(ε0*r^2) Now for the second question b) for r>a : V(r)-V(inf)=- ∫(a^2/(ε0*r^2)dr) [from infinity to r]=[a^2/(ε0*r)]+ (2a/(ε0)) for r

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