imagine that you have 5 conducting thin spherical shells with diameters R, 2R, 3

Question

imagine that you have 5 conducting thin spherical shells with diameters R, 2R, 3R, 4R, and 5R. these 5 thin shells have been nested such that they fit inside each other without touching and are all centered on the same point. the shells have been charged such that the inner most shell has total charge +Q, the second has -Q, the third has +Q, the fourth has -Q and the outer most shell has +Q. you may assume that this configuration allows each sphere to have a uniform charge density that is infinitesimally thin. for each of the following locations determine an expression for the electric field as a function of distance from the common center of the spheres r.
a) 0 < r < R
b) R < r < 2R
c) 2R < r < 3R
d) 3R < r < 4R
e) 4R < r < 5R
e) 5R < r

Explanation / Answer

Here, for the electric field

a) for 0 < r < R

electric field = 0 N.m^2/C

as there is no charge inside the shell

b) for R < r < 2R

electric field = k * (Q)/r^2

electric field = k * Q/r^2

c) 2R < r < 3R

electric field = k * (Q -Q)/r^2

electric field = 0 N.m^2/C

d)3R < r < 4R

electric field = k * (Q -Q + Q)/r^2

electric field = k * Q/r^2

e)

electric field = k * (Q -Q + Q - Q)/r^2

electric field = 0 N.m^2/C

f)

5R < r

electric field = k * (Q -Q + Q - Q + Q)/r^2

electric field = k * Q/r^2

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