Module 2 : Electrostatics
Lecture 10 : Capacitance
  the capacitance is given by
\begin{displaymath}C = \frac{Q}{\phi} = \frac{2\pi\epsilon_0 L}{\ln\frac{R_2}{R_1}}\end{displaymath}
  Work Done in Charging a Capacitor :
  Consider a parallel plate capacitor. The process of charging a capacitor consists of removing negative charges (electrons) from the positive plate and depositing them on the negative plate.
Suppose at a particular instant, the charge on the plates are $\pm q$, so that the potential difference between the plates is $q/C$. To transport an infinitisimal charge $dq$ from the positive plate to the negative plate, the work done by an external agency is
 
\begin{displaymath}dW = \frac{q}{C}dq\end{displaymath}
  Total work done in charging the plates from $q=0$ to $q=Q$is
 
\begin{displaymath}W = \frac{1}{C}\int_0^Qq dq = \frac{Q^2}{2C}\end{displaymath}
  In terms of potential difference $\phi$,
 
\begin{displaymath}W = \frac{1}{2} C\phi^2\end{displaymath}
    
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