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Prove that the gradient of an electric potential V(r) which depends only on the distance r=(x^2 + y^2 + z^2)^1/2 from the origin has the vlaue gradV(r) = V'(r)r-hat where r-hat :=r/r is a unit vector in the direction ofr, and V'(r) := dV(r)/dr. Use this to evaluate the electric field E= -gradV(r) for the Coulomb potential

V(r)= kq/r from a point charge +q, where k=1/(4*pi*E0)

E0 stands for epsilon.

My question is:

I proved that gradV(r) = V'(r)r-hat. How do I evaluate the electric field for the Coloumb potential? Would I take the gradient of V(r)=kq/r? I don't get what I need to do.

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# Homework Help: Electric field

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