The electric field outside any spherically symmetric charge distribution is the

Question

The electric field outside any spherically symmetric charge distribution is the same as if all of the charge were concentrated into a point charge.  Gauss's law can be used to show the electric field inside a spherically symmetric charge distribution is zero if none of the charge is at a distance from the center less than that of the point where we determine the field.

Using the above information, we can find the electric field at any radius for any spherically symmetrical charge distribution. A solid sphere of charge of radius R has a total charge of q uniformly spread throughout the sphere.

    (a) Find the magnitude of the electric field for R ? r. (Use any variable or symbol stated above along with the following as necessary: k for the Coulomb constant.)
    

Explanation / Answer

a) qenc = q

so E = k q/r^2

b) now qenc = q Venc/V = q r^3/R^3

so E = k q r^3/R^3 *1/r^2 = k q r/R^3

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