Question

A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s Law, derive an expression for an electric field at a point outside the shell. Draw a graph of electric field E(r) with distance r from the centre of the shell for 0 < r < ∞.

Answer 1

Answer:

Electric field due to uniformly charged spherical shell is given as

$E = \frac{Q}{4\pi \epsilon_0 r^2}$

Explanation:

As we know by Gauss law of electric field that electric flux due through a closed Gaussian surface is always equal to the ratio of enclosed charge and permittivity of the medium

So we have

$\int E. dA = \frac{q}{\epsilon_0}$

here for conducting sphere of uniform charge if we take a gaussian surface outside it

$E.4\pi r^2 = \frac{Q}{\epsilon_0}$

so we have

$E = \frac{Q}{4\pi \epsilon_0 r^2}$

the graph of electric field is given as

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Topic : electric field

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