Question

Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center,

p(r)=(C/r²)e^-kr

where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q.

a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q.

b) Show that C= kQ /4π(1 − e^-kR)

c)Using Gauss’s law, find the electric field at a distance r≤R, inside the sphere. Does this answer match your results for part (a) on the surface of the sphere,when r = R?

d) Using the differential form of Gauss’s law, check that the electric field that you found gives the correct charge density

Answer 1