Electrostatic Potential and Capacitance - I

Electrostatic Potential at a Point:

It is the work done by per unit charge by an external agency, in bringing a charge from infinity to that point.

Electrostatic Potential due to a Charge at a Point:

The electrostatic potential at a point with position vector r due to a point dipole of dipole
moment p place at the origin is

The result is true also for a dipole (with charges –q and q separated by 2 a) for r >> a.
For a charge configuration q₁, q₂, …… qn with position vectors r₁, r₂, ….r_n, the potential at a point P is given by the superposition principle

where r₁p is the distance between q₁, and P, as and so on.

Electrostatics Potential Energy Stored in a System of Charges:
It is the work done (by an external agency) in assembling the charges at their locations.

Electrostatic Potential Energy of Two Charges q₁, q₂, at r₁, r₂:

where r₁₂ is distance between q₁ and q2

Potential Energy of a Charge q in an External Potential:
V(r)= qV(r)

Potential Energy of a Dipole of Dipole Moment p in a Uniform Electric Field:
E = – p.E.

Equipotential Surface:

An equipotential surface is a surface over which potential has a constant value.
a)For a point charge, concentric spheres centered at a location of the charge are equipotential surfaces.
b)The electric field E at a point is perpendicular to the equipotential surface through the point.
c)E is in the direction of the steepest decrease of potential

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