Chapter 2 : Electrostatic Potential and Capacitance

 

Introduction: Electrostatic potential due to positive charge is q/4πεₒr and physically it requires work to bring another charge at position r to overcome the force of attraction. If unsupported the charge thus brought will be repelled and accelerated away. Similarly, for a negative charge, the potential is given by  (-q)/4πεₒr and it means that we need to prevent a positive test charge from bumping into the negative charge. If unsupported, the negative charges will be attracted and accelerated towards the negative charge. 

A dipole has positive and negative charges of the same magnitude separated by a certain distance which is of the order of angstrom. At the center of the dipole, there is zero potential. The potential of a dipole is zero if the point happens to be equidistant from the positive and the negative charges. So, for a point on the perpendicular bisector, the potential is always equal to zero. However, it will be influenced by either of the charges if the point is closer to them. We generally try to find the potential due to dipole at a general point that is far away from both the positive and negative charges as well as from the center of the dipole. 

For finding the dipole at any point P,  we mark the positions of the positive and negative charge, the position vector of the point from the center of the dipole, and the angle between the position vector and dipole moment. Thereafter, we add the potentials due to the positive and negative charges and use Cosine law and Binomial expansion to get the final expression of Vdiple =P.r/4πεₒr². 

The electric field bears a very good relationship with potential. Mathematically, the electric field is negative of the potential gradient. By using calculus, we can show that E = -dv/dr. Similarly, by using equipotential points and surfaces, we can show that the electric field always goes in the direction of decreasing potential. 
Finally, we winded up the class by creating a system of charges. We discussed that to create a system of charges in a space we need to do work if there is more than one charge.