Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential
 

An intutive form for $U(A,B)$is

\begin{displaymath}U(A,B) = \phi(A) -\phi(B)\end{displaymath}

where $\phi(x)$is a scalar function which depends only on the position $x$. $\phi(x)$is called the electrostatic potential of the position $x$. $\phi(A)-\phi(B)$is the potential difference between the positions $A$and $B$. The absolute value of the potential at a position is meaningless unless we define a reference position at which the potential is zero. Since Coulomb force vanishes only at infinite distances from a source, it is convenient to take infinity to be such a reference position. Thus, the potential at a position $x$is

\begin{displaymath}\phi(\vec x) = -\int_\infty^{\vec x}\vec E\cdot\vec{dl}\end{displaymath}

It may be noted that such a reference point is an inappropriate choice for some infinite distribution of charges (e.g. a line charge) where the field does not fall off fast enough to make the integral above vanish.

 

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