CAPACITANCE AND CAPACITOR

If a potential difference V is applied between two conductors (or plates) placed closed together but insulated from each other, to produce charges +Q and -Q upon them, there is proportionality between the charge and the potential difference,  which is expressed as:

Q ∝ V

or    Q = C ᐧ V

where C is a constant called the Capacitance of the particular set of mutually insulated conductors, their distance apart and on the nature of the insulating material, between them. The insulating material is called the dielectric.

Such a construction of two conducting bodies (whether in the form of plates or spheres) placed close to each other but separated by an insulating material from each other is called a Capacitor or Condenser, and is used for storage of electrical energy.

From the above relation, the capacitance is given by:

C=QV

The charge Q is expressed in coulombs, the potential difference V in volts, then the capacitance C is expressed in farads.

RELATION BETWEEN POTENTIAL GRADIENT AND ELECTRIC INTENSITY

Potential gradient g is defined as:

g=dVdx

                                ..........................................(1)

Electric field E is defined as:

E=−dVdx

                                .........................................(2)    

From equation (1) and (2)

E=−g

This shows that the potential gradient g at a point in the electric field is negative in magnitude of E at that point.

From the point of view of magnitude, both E and g are equal and this can be proved as under:

Since                                    

V=Wg

∴  1 volt=1 joule1 coulomb


But      1 Joule=1 newton×1 meter


∴  1 volt=1 newton×1 meter1 coulomb


or          1 volt1 meter=1 newton1 coulomb


∴  1 volt / meter=1 newton / coulomb


thus     unit of potential gradient=unit of electric intensity

POTENTIAL GRADIENT

DEFINITION: A potential gradient is the space rate of change of potential with distance.

If the dielectric is homogeneous and the electric field is steady and uniform, the potential gradient is a constant.

Potential Gradient is denoted by g.

It is defined as :-

           
g=dVdx

When the potential gradient is a constant,  then 

     
g=Vt volt per unit thickness

where, V = the potential difference between the dielectric of thickness t

Potential gradient is expressed in volts per meter.

EQUIPOTENTIAL SURFACES

Equipotential surface: In electric field surrounding a charged body, there exist points which are at the same potential. A surface on which all such points lie which have the same potential is called an Equipotential surface.

For example :-

In the case of the spherical charged body, any number of points situated at the same distance from its center will have the same potential.

The locus of all such points will also be a sphere and the surface of the sphere will be equipotential surface and obviously, there will be an infinite number of equipotential surfaces in such field.

A particular surface may contain all points having a potential V₁, another surface may contain all points having a potential V₂, and so on.

Thus surface A, B, etc as shown in above figure are equipotential surfaces.