State Gauss’ theorem. Give its mathematical expression. Derive an expression for the electric field intensity at any point due to an infinite plane sheet of charge of uniform charge density $\sigma$ $\mathrm{coulomb}/{\mathrm{metre}}^2$ .

State Gauss’ theorem in electrostatics.
Apply this theorem to derive an expression for the electric intensity due to an infinite sheet of charge and hence deduce the expression for electric intensity due to two parallel oppositely charged thin infinite sheets of charge at a point

(i) between the sheets,

State Gauss’ theorem in electrostatics.
Apply this theorem to derive an expression for the electric intensity due to an infinite sheet of charge and hence deduce the expression for electric intensity due to two parallel oppositely charged thin infinite sheets of charge at a point

(ii) Outside the sheets.

Using Gauss’ theorem derive an expression for the electric intensity due to a charged thin spherical shell at

(i) external point,

(ii) surface point,

(iii) internal point.
Draw the graph showing the variation of electric intensity obtained as above with distance from the centre.

Using Gauss’ theorem, derive an expression for the electric field intensity due to a charged thin spherical shell at Surface point.

Draw the graph showing the variation of electric field intensity obtained as above with distance from the centre.

Using Gauss’ theorem derive an expression for the electric intensity due to a charged thin spherical shell at

internal point.

Draw the graph showing the variation of electric intensity obtained as above with distance from the centre.