Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

 

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) $(–1, \sqrt{3} , 0)$

Find the flux of the electric field through a spherical surface of radius $R$ due to a charge of $8.85 \times {10}^{–8} \mathrm{C}$ at the centre and another equal charge at a point $3R$ away from the centre (Given, ${\mathrm{\epsilon }}_0 = 8.85 \times {10}^{–12}$ units).

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.