Consider a system of charges q

_{1}, q_{2},…, qn with position vectors r_{1}, r_{2},…, r_{n}relative to some origin. The potential V_{1}at P due to the charge q_{1}is_{1P}is the distance between q

_{1 }and

_{P}. Similarly, the potential V

_{2}at P due to q

_{2}and due to q are given by

where r

_{2P}and r_{3P}are the distances of P from charges q_{2 }and q_{3}, respectively; and so on for the potential due to other charges.
By the superposition principle, the potential V at
P due to the total charge configuration is the algebraic sum of the potentials
due to the individual charges

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 q is the total charge on the shell and R its
radius. The electric field inside the shell is zero. This implies that
potential is constant inside the shell (as

**no work is done in moving a charge inside the shell**), and, therefore, equals its value at the surface, which is
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