Expression For Electric Potential at any Point Due to an Electric Dipole
ELECTRIC POTENTIAL AT ANY POINT DUE TO AN ELECTRIC DIPOLE : Obtain expression for the electric potential at any point due to an electric dipole. Rewrite this expression if point of observation lies on the (i) axial line of the dipole and (ii) equatorial line of the dipole. Consider any point P at a distance r from the centre (O) of the electric dipole AB. Let OP make an angle $\theta$ with the dipole moment $\vec{p}$. Let $r_1$ and $r_2$ be the distances of point P from -q charge and +q charge of the dipole respectively. Step 1. Potential at point P due to -q charge is given by $V_1 = \frac{1}{4\pi\epsilon_0} \frac{(-q)}{r_1}$ Potential at point P due to +q charge is given by $V_2 = \frac{1}{4\pi\epsilon_0} \frac{q}{r_2}$ $\therefore$ Using principle of superposition, potential at point P due to the dipole is given by $V = V_1 + V_2$ or $V = -\frac{1}{4\pi\epsilon_0} \frac{q}{r_1} + \frac{1}{4\pi\epsilon_0} \frac{q}{r_2}$ $V= \frac{q}{4\pi\epsilon_0} \left[ \frac{1}{r_2} - \frac{1...
