Module 2 : Electrostatics
Lecture 10 : Capacitance
Capacitance

Consider a spherical conductor of radius $R$ carrying a charge $Q$. The potential of the sphere is given by

\begin{displaymath}\phi = \frac{Q}{4\pi\epsilon_0 R}\end{displaymath}

The potential of the conductor is proportional to the charge it contains. This linear relationship is true in general, independent of the shape of the conductor,

\begin{displaymath}Q= C\phi\end{displaymath}

The constant of proportionality $C$ is called the capacitance of the conductor. For the conducting sphere the capacitance is $4\pi\epsilon_0 R$.

    Unit of capacitance :
  The M.K.S. unit of capacitance is Coulomb/Volt which is called a Farad. However, one Farad turns out to be very large capacitance (the capacitance of the Earth is approximately 700 micro-Farad). A more practical unit of capacitance is a micro-Farad ( $\mu F$) or a pico- Farad (pF) :
 
\begin{eqnarray*} 1 \mu F &=& 10^{-6} F\\ 1 pF &=& 10^{-12} F \end{eqnarray*}
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