Three point charges $–Q, Q$ and $Q$ are placed on a straight line with distance $d$ between charges as shown. Find the magnitude of the electric field at the point $P$ in the configuration shown which is at a distance a from middle charge $Q$ in the system provided that $a\gg d$. Take $2Qd=p$.

 

A charge $q$ is carried slowly from a point $A (r, 135º)$ to a point $B (r, 45º)$ Following a path which is a quadrant of circle of radius $r$. If the dipole moment is $p$ , then find out the work done by external agent.

Find out the magnitude of electric field intensity and electric potential due to a dipole of dipole moment, $\stackrel{\rightharpoonup }{P}=\hat{\mathrm{i}}+\sqrt{3}\hat{\mathrm{j}}$ kept at origin at following points.

(i) $(2, 0, 0)$

(ii) $(–1, \sqrt{3} , 0)$

A charge $\mathrm{q}$ is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss’s law, find the electric flux due to this charge through the given surface.

The figure shows two conducting spheres separated by a large distance and of radius $2 \mathrm{cm}$ and $3 \mathrm{cm}$ containing charges $10 \mathrm{\mu C}$ and $20 \mathrm{\mu C}$, respectively. When the spheres are connected by a conducting wire, find out the following

$\left(\mathrm{i}\right)$ The ratio of the final charges.

$\left(\mathrm{ii}\right)$ Final charge on each sphere. 

$\left(\mathrm{iii}\right)$ The ratio of final charge densities.