Module 2 : Electrostatics
Lecture 10 : Capacitance
 Capacitor :
  A capacitor is essentially a device consisting of an arrangement of conductors for storing charges. As a consequence, it also stores electrostatic energy. The simplest capacitor consists of two conductors, one carrying a charge $Q$and the other a charge $-Q$. Let $\phi_1$be the potential of the first conductor and $\phi_2$that of the second. Since the conductor is an equipotential surface, the potential difference between the conductors $\phi_1-\phi_2$is also constant, and is given by
\begin{displaymath}\phi_1-\phi_2 = -\int_2^1 \vec E\cdot \vec{dl}\end{displaymath}
  where the line integral is carried out along any path joining the two conductors. The electric field is proportional to the charge $Q$since if the charge on each conductor is multiplied by a constant $\alpha$, the charge density and hence the electric field also gets multiplied by the same factor. Thus $Q$is proportional to the potential difference $\phi=\phi_1-\phi_2$
 
\begin{displaymath}Q= C\phi\end{displaymath}
  where $C$is the capacitance of the conductor pair.
  A capacitor consisting of a single conductor (like the spherical conductor described above) may be considered to be one part of a conductor pair where the second conductor containing the opposite charge is at infinity.
   
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