A non-conducting sphere of radius R has charge density rho(r) = beta4 with beta

Question

A non-conducting sphere of radius R has charge density rho(r) = beta4 with beta > 0. What is the magnitude of E inside the sphere (for r R)? Draw a plot of the E-field magnitude as a function of r. Clearly label your plot and indicate the following on your sketch: the r-dependence of the E-field magnitude inside and outside of the sphere and the maximum value of the E-field magnitude.

Explanation / Answer

The electric field is E=Q r/4pi e0 R^3 Note that the limit at r= R agrees with the expression for r >= R. The spherically symmetric charge outside the radius r does not affect the electric field at r. It follows that inside a spherical shell of charge, you would have zero electric field. EDIT: r=R/2 as it is half way b/w the sphere and its surface.

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