Question

A thin aluminum sphere of radius 25 cm has a charge of Q=150 nC uniformly distributed on its surface.

a) Assuming that the center of the sphere is at r=0, find expressions for the electric field for all regions of interest (r<R, and R>r), and make a plot of the electric field strength as a function of r.

b) Find expressions for the electric potential for all regions of interest, and plot the electric potential as a function of r. Choose as a reference point V=0 for r=?.

c) How much work, in Joules, is needed to bring a proton from infinity to the surface of the sphere?

d) If a small hole is made in the sphere, how much extra work is required to bring the proton in through the hole to r=0 (from the surface of the sphere to the center)?

Answer 1

PART A)

Electric field inside the sphere is given by (r<R)

As there is no enclosed charge inside the sphere and all charge reside on the outer surface

If point is outside the surface (r > R)

PART B)

If point is inside the surface (r < R)

Since E = 0 inside the surface

then potential will remains constant as it is on its surface

When point is outside the surface (r > R)

V = 0 at r = infinite large distance from centre of sphere

PART C)

Work done to bring the charge is given by

PART D) since potential inside the sphere will remain the same so there is no extra work to do to bring it at r = 0