Applications of Gauss’ Theorem(Field Due to a Uniformly Charged Thin Spherical Shell)

Chapter-1|Electric Charges and Fields | NCERT 12th Physics:

(III) Field Due to a Uniformly Charged Thin Spherical Shell:

Let σ be the uniform surface charge density of a thin spherical shell of radius R. The Gaussion surface will be a spherical surface centred at the centre of shell.

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(a) At a point outside the Shell: (r>R)

Since E and n^ are in the same direction, So θ=0
Flux through the Gaussian surface-

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(b) At the point on the surface of the Shell:(r=R)


(c) At the point inside the Shell:

Since the charges inside the gaussian surface is zero.

Since the charges inside the gaussian surface is zero.

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Hence, Electric field due to a uniformly charged spherical shell is zero at all points inside the shell.

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