Electrostatic Potential: Meaning, Working Principle, Equations & SI Unit

Electrostatic potential is the work done by an external agent to bring a unit positive charge from infinity to a point without changing its kinetic energy. 

When speaking of calculating electrostatic potential, it means we measure the amount of electric potential energy a unit charge would have at a point in the electric field. 

Let’s understand two key terms here. 

Electric Potential Energy - This is the energy a charge has due to its position in the electric field.
Referring to Physics basics, such as the difference between potential and kinetic energy, you will notice that this concept is like gravitational potential energy. 

The fundamental behind it is the higher you lift an object from the centre of gravity, the more enery it will have. Likewise, when you move a charge against the electrical field, the more electric potential energy it will have.   

Unit Charge - This simply refers to one coulomb of electric charge. 

By the above electrostatic potential definition, we are imagining how much energy one coulomb of charge would have at a specific point. That makes the electrostatic potential a per-charge quantity.

Importance of Learning Electrostatic Potential for National Exams

• This is an essential concept covered in various exam syllabi - CUET, IAT, etc. In exams like JEE Main, its weightage is around 6%. 
• Electrostatic potential is the building block to understanding electromagnetism, particularly the concept of charge distribution that discusses how electric charges are arranged in space. This is important to learn in electrical engineering. 

In your CBSE Physics textbook, this is the second section of the chapter. The definition of electrostatic potential is

“Work done by an external force in bringing a unit positive charge from infinity to a point = electrostatic potential (V) at that point.”

Why Infinity? Infinity is a reference point where the electrostatic potential is considered zero.

Also, while preparing for CBSE Board exam, check out the free NCERT Solutions for the 2nd Chapter.  

Let’s go a little deeper to see how energy moves in electric fields. 

We established above, electrostatic potential is like gravity, which is a conservative force. 

The work done by a conservative force in moving a charge between two points depends only on the initial and final positions. In that logic, the charge movement is independent of the path. 

Because the force is conservative, we can define an electrostatic potential energy (U) associated with the position of a charge in an electric field. 

If you move a charge against the electric field, or let’s say push a positive charge toward another positive charge, you’re doing positive work. This work is stored as potential energy.

We say it as

$$\text{Work by external force}=∆U=U_{\text{final}}-U_{\text{initial}}$$

 

Within an electrostatic field, the electric potential at a point $P$ is defined as the work done by an external agent in taking a unit point positive charge from a reference point (generally taken at infinity) to that point $P$ without changing its kinetic energy.

Let's see how we represent it mathematically. 

If $(W\mathrm{\infty }\to P)$ ext is the work required in moving a point charge $q$ from infinity to a point $P$ , the electric potential of the point $P$ is

${\left.{\mathrm{V}}_{\mathrm{p}}=\frac{{\left.{\mathrm{W}}_{\mathrm{\infty }\to \mathrm{p}}\right)}_{\mathrm{e}\mathrm{x}\mathrm{t}}}{\mathrm{q}}\right]}_{\mathrm{\Delta }K=0}=\frac{{\left(-{\mathrm{W}}_{\mathrm{e}\mathrm{l}\mathrm{c}}\right)}_{\mathrm{\infty }\to \mathrm{p}}}{\mathrm{q}}$

Note:

• ${\mathrm{W}}_{\propto \to \mathrm{P})\text{ext}}$ can also be called as the work done by external agent against the electric force on a unit positive charge due to the source charge.
• We write both W and q with proper sign.

If we know the potential at some point (in terms of numerical value or in terms of formula) then we can find out the work done by electric force when charge moves from point ' $P$ ' to $\mathrm{\infty }$ by the formula

${\left.W_{\text{ep}}\right)}_{p\to \mathrm{\infty }}=q{V}_p$

 

The S.I. Unit of Electrostatic Potential is Volt $=\frac{\text{joule}}{\text{coulmb}}$ and its dimensional formula is $\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}\right]$ .

 

Name / Type	Formula	Note	Graph
Point charge	kq/r	q is source charge. r is the distance of the point from the point charge.
Ring (uniform/nonuniform charge distribution)	at centre: kq/r at the axis: s:KQ/√R2+x2	Q is source chage. x is the distance of the point on the axis from centre fring
Uniformly charged hollow conducting/nonconducting /solid conducting sphere	for r >= R, V = kQ/r for r <= R, V =kQ/R	R is radius of sphere r is the distance from centre of sphere to the point Q is total charge .= 4πR2

Uniformly charged solid nonconducting sphere.	For r >= R, V = KQ/r For r <= R V= KQ (3R2-R2)/2R3 = P/6ε₀(3R2-R2)	* R is radius of sphere *  r is distance from centre to the point vcenter = 3/2 V surface  Q is total charge . = p 4/3πr3 * Inside the sphere potential varies parabolically * Outside the sphere potential varies hyperbolically.
Infinite line charge	Not defined	*Absolute potential is not defined. * Potential difference between two points is given by formula:
Infinite nonconducting thin sheet	Not defined	*Absolute potential is not defined. * Potential difference between two points is given by formula VB - VA = -2Kλln(rB/rA)
Infinite charged conducting thin sheet	Not defined	*Absolute potential is not defined. * Potential difference between two points is given by formula VB - VA = - σ/ε₀(rB-rA)