NEET Physics Notes Electrostatics-Electric Potential

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 [ML²T^-3A^-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 q₁ q₂, q₃,… 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 q₃ and q₂ separated by distance r₁₂ , the potential energy is given by

For a system of three charges q₁  q₂ and q₃  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.

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