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, ….rn, 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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