Electric Potential

The electric potential is a scalar quantity which is generally denoted by φ, φE or V. It is also termed as electric field potential or the electrostatic potential. In simple words electric potential refers to the amount of work required for moving a unit charge from the reference point to a particular point against the electric field.

The electric potential at any point is equal to the quotient of the electric potential energy of the particle and the charge of the particle at a particular point. The potential energy is measured in joules while the charge is measured in coulombs.  The potential may be calculated in either a static or a dynamic electric field and as described above its unit is joules per coulomb i.e. JC-1 or volts V. another term that is associated with this concept is generalized electric scalar potential which is used in thermodynamics. But it cannot be interpreted in the same way as the electric potential.

The potential energy for a positive charge has inverse relationship with electric field. The energy increases when it moves against an electric field and falls when it moves with the electric field. For a negative charge, the situation is quite opposite.

Amount of work done in moving unit positive charge from infinity up to the point under consideration against the field of a given charge q is also defined as the electric potential.

In other words, it is negative of the work done by the internal forces

It is a scalar quantity

(i) Potential at a point due to several charges

v = v1 + v2 + v3 +….

(ii) Electric Potential due to electric dipole

v = P cos θ / 4π∈0 (r2-a2 cos2 θ)

For r≫ a

v = P cos θ / 4π∈0 r2                                           

Potential due to a uniformly charged disc
(i) At a point on its axis

v = σ/2∈0 . {(R2 + x2)1/2 – x}

where σ = surface charge density on disc

(ii) At the centre of the disc

v = σ/2∈0. R

(iii) Potential at the edge of a uniformly charged disc

v = σR/ π∈0

Potential at the apex of a cone having charge Q distributed uniformly on its curved surface and having slanting length L

v = Q / 2π∈0 L

Potential of a conducting sphere of radius R at a distance r from the centre

(i) r > Rv = Kq/r, where q is the charge on the sphere

(ii)r = Rv = Kq/r , where K = 1/ 4π∈0

(iii)r < Rv = Kq/r

Potential of a dielectric sphere

(i)r > R

then v = Kq/r, where q is the total charge in the dielectric sphere

(ii)r = R

then v = Kq/R

(iii)r < R

then v = Kq/2R. [3-r2/R2

Torque on a dipole in presence of external electric field
Torque = qE. 2a sin θ
τ¯= PE sin θ
Potential Energy U =  -P¯.E¯

The concept of electric potential is very beneficial in studying electrical phenomena. If the electric field is defined to be the force per unit charge, then the electric potential can be assumed to be the potential energy per unit charge. As a result, the work done in shifting a unit charge form one particular point or place to another obviously within the same electric circuit is the same as the difference in the potential energies at each point.

Let us consider an illustration on fining out the potential difference between two conducting spheres.

Example: Two conducting spheres having radii a and b charged to q1 & q2 respectively.  Find the potential difference between 1 & 2?

Two Conducting spheres with radii a and b

Solution: The potential on the surface of the sphere 1 is given by

This video will further clear your concepts on the topic

Electric Potential Energy

The electric potential energy of a system of point charges is the amount of work done in bringing the charges from infinity in order to form the system. For point charges q

1 and q2 separated by a distance r12, Electric potential energy of the system q1 and q2 is given by

U = q1q2/ 4π∈0r12

For three particle system q1, q2 and q3

U = 1/ 4π∈0 (q1q2/r12 + q1q3/r13 + q2q3/r23)

We can define electric potential (VP) at any point P in an electric field as

VP = UP/q

where Up, is the change in electric potential energy in  bringing the test charge q0from infinity to point P

Example: Determine the interaction energy of the point charges of the following set- up 

askIITians offers comprehensive study material which covers various physics questions of IIT level. It also covers numerous electric potential JEE problems. The topic of electrostatic potential is very important for JEE it is is vital for the JEE aspirants to have a good hold on questions like potential at pex of cone or potential due to disc. 

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