Capacitance (C)- Farads

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When two conductors are embedded in a homogeneous dielectric medium as shown in the figure

$M_{2}$ – conductor 2 carries a positive charge (+Q) and $M_{1}$ -conductor 1 carries a negative charge (-Q). Assume the two charges are equal.

$\therefore$ The resultant charge is zero.

we know that charge is carried on the surface as a surface charge density $\rho _{s}$ and $\overrightarrow{E}$ is normal to the conducting surface.

since $M_{2}$ carries positive charge the flux is directed from $M_{2}$ to $M_{1}$ . flux starts from positive charge and ends at negative charge.

i.e, flux lines leaving one conductor must terminate at the surface of the other conductor.

$\therefore$ a field is induced between the two conductors $M_{2}$ and $M_{1}$ and the medium between these two conductors is a dielectric material.

Now, work must be done to carry a positive charge from $M_{1}$ to $M_{2}$ , that is opposite to the induced field.

$V_{21}= -\int_{2}^{1}\overrightarrow{E_{induced}}.\overrightarrow{dl}$

$V_{21}=V_{1}-V_{2}$ .

$V= -\int_{2}^{1}\overrightarrow{E_{induced}}.\overrightarrow{dl}$ .

Now, a system as shown in the above figure will have a special physical property called capacitance.

Definition of Capacitance of a conductor:-

The capacitance of a conductor is defined as the physical property of the conductor which is the ability to store Electrical Energy

i.e, $C=\frac{Q}{V}$ Farads

(or)

Capacitance is the ration of charge of the conductor (either m $M_{1}$ (or) $M_{2}$ ) to the voltage applied between the two conductors.

Procedure to find Capacitance:-

Assume Q and determine V in terms of Q , or else assume V and determine Q in terms of V.
choose a suitable Co-ordinate system.
assume the two conducting plates are carrying charges +Q and -Q.
Determine using Gauss’s law (or) by using Coloumb’s law and find $V= - \int \overrightarrow{E}.\overrightarrow{dl}$ .
Finally calculate $C=\frac{Q}{V}$ .

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Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems. View all posts by Lakshmi Prasanna Ponnala