Text Based Exercises

Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative.

State the theorem which relates total charge enclosed within a closed surface and the electric flux passing through it. Prove it for a single point charge.

An 'atom' was earlier assumed to be a sphere of radius a having a positively charged point nucleus of charge $+Ze$ at its centre. This nucleus was believed to be surrounded by a uniform density of negative charge that made the atom neutral as a whole. Use this theorem to find the electric field of this 'atom' at a distance $r(r<a)$ from the centre of the atom.

Define electric flux quantity?

A point charge $q$ is at a distance of $\frac{d}{2}$ directly above the centre of a square of side $d$, as shown in Fig. 1.163. Use Gauss' law to obtain the expression for the electric flux through the square.

If the point charge is now moved to a distance ‘$d$’ from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected.

Use Gauss' law to derive the expression for the electric field $\left(\overrightarrow{E}\right)$ due to a straight
uniformly charged infinite line of charge density $\raisebox{1ex}{${\displaystyle \mathrm{\lambda } \mathrm{C}}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.$.

Draw a graph to show the variation of $E$ with perpendicular distance $r$ from the line of charge.

Find the work done in bringing a charge $q$ from perpendicular distance $r_1$ to $r_2$ ($r_2>r_1$).