Answer the following questions about the electric potential of a short dipole of charges ±q separated by distance 2a in free space.
a. (i) Starting from the definition of electric potential as work done per unit test charge, derive an expression for the potential at a distant point whose position vector makes an angle θ with the dipole axis.
b. (ii) Compare the distance-dependence of the potential of a dipole with that of an isolated point charge. Explain physically why the two dependences differ.
c. (iii) A dipole of moment 2.5×10−8Cm produces a potential of 200V at a point on its axis in air. Calculate the distance of this point from the centre of the dipole.