  Electrostatic Potential And Capacitance

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1

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.
2

Electric potential due to a point charge  where is a point charge and is the potential due it at a point of r distance.
Two charges and are kept apart. Then at any point on the perpendicular bisector of line joining the two charges:
A
the electric field strength is zero
B
the electric potential is zero
C
both electric potential and electric field strength are zero
D
both electric potential and electric field strength are non-zero
3

Potential due to an infinitely long uniformly charged wire  where is the length of the wire, and is the perpendicular distance from the wire where the potential is calculated
4

Potential due to a uniformly charged disc  where is the surface charge density
5

Potential energy of a system of two charges in an external field

Example:
Electric field in a region is given as . A charge of C is placed at and a charge of C is placed at . Find the total energy of the system of charges.
Assume potential at is zero.
Solution:

At
At
Potential energy of system,
Substituting values,
6

Electric fields for a parallel plate capacitor  For the outer region,

For the inner region i.e. the region between the plates,

where is surface charge density, is area of cross section.
7

Factors affecting capacitance

The capacitance depends only on:
1. The shape and size of capacitor plates - Geometric configuration
2. The distance between 2 plates - Separation distance
3. The medium present between 2 plates
In a parallel plate capacitor, the capacitance:
A
increases with increase in the distance between the plates
B
decreases if a dielectric material is put between the plates
C
increases with decrease in the distance between the plates
D
increases with decrease in the area of the plates
8

Capacitance of an isolated spherical conductor

The potential of a charged conducting sphere is given by where is the radius of the sphere.
Then
Now for an isolated spherical conductor, taking limits as and , we have
9

Capacitors in parallel  The effective capacitance of capacitors in parallel is :
In parallel combination voltage remains same across caapcitors only charge gets divided. so,

10

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

11

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.
In electrostatic generators, charges
A
of only one sign can be produced
B
produced are always in opposite pairs
C
are not produced.
D
None of these