Question

Using gauss law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radus R at a points (¡)outside the shell (¡¡)inside the shell Plot a graph showing variations of electric field as a function r>Rand r<.{ r being the distance from the centre of the shell }

Answer 1

Answer:

Explanation:

Let's calculate electric field at the point P at a distance r (r > R) from its centre. Draw the Gaussian surface through point P so as to enclose the charged spherical shell. The Gaussian surface is a spherical shell of radius r and centre O.

(i) When r>R

Let E be the electric field at point P(outside the surface) then,

dФ=E.dA (A is Area vector)

*Electric fields from center of a sphere is always normal to the suface and will be along the area vector(A)

∴dФ=EdAcos 0

dФ=EdA

integrating on both sides

Ф=∫EdA (0 -> A)

Ф=E∫dA (E is a constant)

∫dA= 4πr²

∴ Ф= E× 4πr²

By gauss law, we know that,

Ф=q/ε0

∴E× 4πr²=q/ε0

E=q/(ε0×4πr²)

(ii) When point P lies inside the spherical shell(r<R),there is no enclosed charge, ∴  E× 4πr²=0

and E=0