Let σ be the uniform surface charge density of a thin spherical shell of radius R Field outside the shell.
Consider a point P outside the shell at a distance r from the centre of the shell. Imagine a gaussian sphere of radius ‘r’ The electric flux at P due to surface ∆S is
∆φ= \(\vec E. \vec{\Delta S}\) = E∆S COSθ = E∆S {COS θ = 1}
Total electric flux due to the sphere is
φ = E4πr2 ……….(1)
From Gauss law the electric flux
\(\varphi = \frac{1}{\varepsilon_0}\) total charge = \(\varphi=\frac{1}{\varepsilon_0}q\)
where q = total charge enclosed by the surface From (1) & (2)
E4\(\pi\)r2 = \(\frac{1}{\varepsilon_0}q\) \(\vec E\) = \(\frac{1}{4\pi \varepsilon_0}\frac{q}{r^2}\hat r\)
b) electric field inside shell E = 0