CBSE Class 12 · 2006 · All India · ElectrostaticsShort Answer

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Using Gauss's theorem, show mathematically that for any point outside the shell, the field due to a uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre. Why do you expect the electric field inside the shell to be zero according to this theorem?

Solution

Take a concentric spherical Gaussian surface of radius

r > R

E

is radial and uniform over it (flux

E \cdot 4 π r^{2}

), and it encloses the whole charge

q

E (4 π r^{2}) = \frac{q}{ε _{0}}

E = \frac{1}{4 π ε _{0}} \frac{q}{r ^{2}}

the same as a point charge

q

at the centre.
For a surface inside the shell (

r < R

) the enclosed charge is zero:

E (4 π r^{2}) = 0 \Rightarrow E = 0

so the field is zero everywhere inside.

CBSE Class 12 Board · 2006 · All India · Subjective

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