How Does Charge Distribution Affect Electric Field and Potential in a Sphere?

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A uniformly charged sphere with radius R and total charge Q exhibits an electric field E outside the sphere equivalent to that of a point charge Q. Inside the sphere, the electric field is directed radially outward, with a strength given by Ein = (1/4*pi*epsilon0)*(Q/R^3)*r. The electric potential outside the sphere mirrors that of a point charge, while the potential inside can be derived from the electric field. The ratio of the electric potential at the center to that at the surface is also discussed. Graphs for both electric field and potential as functions of distance are suggested for further analysis.
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Consider a uniformly charged sphere of radius R and total charge Q. The electrical field E(out) outside the sphere (r>R) is simply that of a point charge Q. Gauss's law was used to find E(in) inside the sphere(r<R) is radially ouwards with the field strength

Ein = (1/4*pi*epsilon0)*(Q/R^3)*r


A) Graph E vs r for 0<r<3R
b) The electric potential Vout outside the sphere is that of a point charge Q. Find an expression for the electric potential Vin at position r inside the sphere.
c)What is the ration Vcentre/Vsurface
d) Graph V vs r for 0<r<3R
 
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