CBSE Class 12 · 2016 · All India · ElectrostaticsShort Answer

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Find the electric field intensity due to a uniformly charged spherical shell at a point
(i) outside the shell and
(ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.

Solution

Take a concentric spherical Gaussian surface of radius

r

. (i) For

r \geq R

the whole charge

q

is enclosed:

E \cdot 4 π r^{2} = \frac{q}{ε _{0}}

, so

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

. (ii) For

r < R

the enclosed charge is zero, so

E = 0

. The field is zero inside, rises to

\frac{1}{4 π ε _{0}} \frac{q}{R ^{2}}

at the surface, and then decreases as

1/ r^{2}

outside.

CBSE Class 12 Board · 2016 · All India · Subjective

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