Sunday, 5 February 2017

Electrostatic potential

Electrostatic force is a conservative force, i.e., the work done by the force in moving a unit test charge from one point to another, is independent of the path.
Unit of Potential
J/C is called volt
Potential is a scalar quantity.
Potential Function satisfies Superposition Principle

The gradient of potential gives the electric field.
Potential difference:
The electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy.
Electric potential at a point due to a point charge:
Let  be an isolated point charge situated in air at O. P is a point at a distance r from . Consider two points A and B at distances  from the point O.

The potential difference between A and B is,

The negative sign indicates that the work is done against the electric force.
The electric potential at the point P due to the charge  is the total work done in moving a unit positive charge from infinity to that point.

Two charges at A and  at B separated by a small distance 2d constitute an electric dipole and its dipole moment is p. Let P be the point at a distance r from the midpoint of the dipole O and θ be the 

angle between PO and the axis of the dipole OB. Let r1 and r2 be the distances of the point P from  and  charges respectively.

Potential at P due to charge

Potential at P due to charge

Total potential at P due to dipole is,

Applying cosine law,
By substituting and simplifying,

Special cases :
1. When the point P lies on the axial line of the dipole on the side of , then

2. When the point P lies on the axial line of the dipole on the side of , then

3. When the point P lies on the equatorial line of the dipole, then,

Equipotential Surface:

If all the points of a surface are at the same electric potential, then the surface is called an equipotential surface.

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