Derive an expression for the electric field at a distance r from the center of a

Question

Derive an expression for the electric field at a distance r from the center of a sphere of radius R that carries a uniform volume charge density rho. (a) Find the electric field at the center, a point halfway to the edge, and a point at the edge (A, B, and C, respectively as shown in the figure). Now consider scooping out a spherical cavity of radius R/2 as shown. Convince yourself that this is equivalent to adding a sphere with radius R/2 that has a negative charge density -rho. (b) Find the electric field at the same three points. A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius r_b. When a potential difference is applied between the spheres,

Explanation / Answer

a) Electric field at point C from the centre would be found by using Guasses law ...According to the Gausses law the the total electric flux through close surface is 1/ episilon0 of total charge encloase by that surface.

E . A = Q / epsilon

E = Q / 4pi R2 epsilon

This is the value of electric fild at point C. At point A and B electric field would be eqal to zero becasue electric field inside a conductor having charge resiting on the surface would alwasy be equal to zero.

b) Electric field will remain same as in part a) for the point C , and rest of the two points electric field would be equals to zero.

  

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