Electrostatic Potential And Capacitance

- Learn important concepts of the chapter

Capacitors and their examples

A capacitor is a system of two conductors separated by an insulator used to store electrical energy temporarily in an electric field. For example, on printed circuit boards two wires running parallel to each other on opposite sides of the board form a capacitor. 

A capacitor works in

A.C. circuits only
D.C. circuits only
both A.C & D.C
neither A.C. nor in D.C. circuit.

Capacitors in series

post image
The effective capacitance of capacitors in series is 
The charge q flowing through the caapcitor is same in series combination, only voltage is divided.


Force between the plates of a capacitor

The capacitance C is given by :

Energy stored in caapcitor is
Differentiating this with respect to distance d:

Force of attraction
and Q=CV, so

Discuss and explain the relation between electric field intensity and potential

The relationship between electric field and scalar potential is given as:
, where gradient operator.

Potential due to a dipole at a general point

Potential due to a dipole is given by:

electric dipole moment
angle made by the line joining center of dipole and the point with the dipole moment vector
distance between the center of dipole and the point
Approximation is made that the length of dipole is negligible as compared to the distance of the point from the dipole.

Electric potential

Electric potential () at a point is defined as the amount of work done in bringing a unit positive charge from infinity to that point.
Unit of potential is .

Note: Potential is taken to be zero at infinity and at ground.

An electron and a proton move through a potential difference of . Then:

electron gains more energy
proton gains more energy
both gain same energy
none of them gain energy

Electric potential energy

Electric potential energy of charge q at a point (in the presence of field due to any charge configuration) is the work done by the external force (equal and opposite to the electric force) in bringing the charge q from infinity to that point.


Equipotential surfaces

Surfaces having same potential are termed as equipotential surfaces
The properties of equipotential surfaces can be summarized as follows:
  • The electric field lines are normal to the equipotentials and are directed from higher to lower potentials. 
  • By symmetry, the equipotential surfaces produced by a point charge form a family of concentric spheres, and for a constant electric field, a family of planes normal to the field lines. 
  • The tangential component of the electric field along the equipotential surface is zero, otherwise non-vanishing work would be done to move a charge from one point on the surface to the other.
  • Work done in moving a particle along an equipotential surface is zero. 
Some equipotential surface are shown in the figure. The magnitude and directions of the electric field is
making angle with the x-axis
making angle with the x-axis
making angle with the x-axis
None of the above

Van de Graff generator

A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. It produces very high voltage direct current (DC) electricity at low current levels.
A simple Van de Graaff generator consists of a belt of rubber (or a similar flexible dielectric material) running over two rollers of differing material, one of which is surrounded by a hollow metal sphere. Two electrodes, in the form of comb-shaped rows of sharp metal points, are positioned near the bottom of the lower roller and inside the sphere, over the upper roller. One comb is connected to the sphere, and another comb to ground. The method of charging is based on the triboelectric effect, wherein simple contact of dissimilar materials causes the transfer of some electrons from one material to the other.
When a long-haired woman puts her hands on a Van de Graaff generator a large conducting sphere with charge being delivered to it by a conveyer belt make her hair stands on end. Which of the following explains this phenomenon?
Like charges attract
Like charges repel
Her hair will not stand on end
Her body is conducting a current to the ground
The Van de Graaf generator makes a magnetic field that draws her hair up on end