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# Electrostatics: Field due to chargespherical shells

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A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of +2q, and the outer shell has a total charge of +4q.

a) Calculate the electric field (magnitude and direction) in terms of q and the distance r
from the common centre of the two shells for i) r < a; ii) a < r < b; iii) b < r < c; iv) c < r < d, and v) r > d. Show your results as a graph.

b) What is the charge on the inner and outer surfaces of both the small and large shells?

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##### Solution Summary

Two charge spherical conducting shells of radii a, b, c, d are concentric and charged with 2q and 4q. Field at every point of space is calculated. The field-position graph is also plotted.

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A small conducting spherical shell with inner radius 'a' and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of +2q and the outer shell has a total charge of +4q.

a) Calculate the electric field (magnitude and direction) in terms of q and the distance r
from the common centre of the two shells for i) r < a; ii) a < r < b; iii) b < r < c; iv)
c < r < d and v) r > d. Show your results as a graph.

b) What is the charge on the inner and outer surfaces of both the small and large shells?

a) Here the charges and the electric field are symmetrical about the center of the spherical shells, hence the electric flux is radial and it is easy to use Gauss' law to find the field at any point in the space.

According to Gauss' law, the electric flux through a closed surface is , where qi is the charge enclosed within the closed surface. The field strength at a point in the field is the flux per unit area normal to the surface.

The mathematical form of Gauss' law is given as

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