**NEET Physics Notes Electrostatics-Electric Potential**

**Electric Potential**

**Electric Potential**

Electric potential at a point in an electric field is defined as the amount of work done in bringing a unit positive charge, without any acceleration, from infinity to that point, along any arbitrary path. Mathematically, if W work is to be done to bring a test charge q0 from infinity to a point, then the potential of that point, is

SI unit of potential is volt, where

dimensional formula is [ML^{2}T^{-3}A^{-1}]. Electric potential is a state function and does not depend on the path followed.

**Electric Potential Due to a Point Charge**

Potential due to a point charge Q, at a distance r is given by

**Electric Potential Due to a System of Charges**

If a number of charges q_{1 }q_{2}, q_{3},… are present in space, then the electric potential at any point will be

**Electric Potential Due to an Electric Dipole**

At any general point,

**Electric Potential due to Some Common Charge Distributions**

Potential at a point distant r from an infinitely long wire having linear charge density λ, is

For a charged conducting sphere/shell having total charge Q and radius R, the potential at a point distant r from the centre of the sphere/shell is

For a charged non-conducting (dielectric) sphere of radius R, the charge Q is uniformly distributed over the entire volume.

Hence,

**(i)**

**Electric Potential Energy**

The electric energy of a system of charges is the work that has been done in bringing those charges from infinity to near each other to form the system. For two point charges q_{3} and q_{2} separated by distance r_{12} , the potential energy is given by

For a system of three charges q_{1} q_{2} and q_{3} are placed at three comers of a triangle (figure), then the electric potential energy of the system will be given by

**Relation between E and V**

Because E is force per unit charge and V is work per unit charge. E and V are related in the same way as work and force. If is the increase in potential over a short displacement

Thus, the electric field intensity E is the negative gradient of potential. This means that decrease in potential is along the direction of E. The SI unit of E is therefore, volt per metre (Vm^{-1})

**Equipotential Surface**

For a given charge distribution, an equipotential surface is the locus of the all the points having the same electric potential. For a point charge or a spherical charge distribution, equipotential surfaces are concentric spheres as shown in figure.

For a uniform electric field, the equipotential surfaces are planes perpendicular to the direction of electric field.

There is no component of electric field along an equipotential surface.

As a result, work done in moving a charge along an equipotential surface, is always zero,

Equipotential surface may be planar, solid etc. But equipotential surface can never be point size. .

Equipotential surface is single valued. So, equipotential surfaces never cross each other.

Electric field is always perpendicular to equipotential surface.