2.5 POTENTIAL DUE TO A SYSTEM OF CHARGES
Potential at a point due to a system of charges is the sum of potentials due to individual charges.
Consider a system of charges
Similarly, the potential
where
If we have a continuous charge distribution characterised by a charge density
We have seen in Chapter 1 that for a uniformly charged spherical shell, the electric field outside the shell is as if the entire charge is concentrated at the centre. Thus, the potential outside the shell is given by
where
Example 2.2
Two charges
Let
If
Example 2.3
Figures 2.8 (a) and (b) show the field lines of a positive and negative point charge respectively.
(a)Give the signs of the potential difference
(b)Give the sign of the potential energy difference of a small negative charge between the points
(c)Give the sign of the work done by the field in moving a small positive charge from
(d)Give the sign of the work done by the external agency in moving a small negative charge from
(e)Does the kinetic energy of a small negative charge increase or decrease in going from
(a) As
(b)A small negative charge will be attracted towards positive charge. The negative charge moves from higher potential energy to lower potential energy. Therefore the sign of potential energy difference of a small negative charge between
Similarly,
(c)In moving a small positive charge from
(d)In moving a small negative charge from
(e)Due to force of repulsion on the negative charge, velocity decreases and hence the kinetic energy decreases in going from