Electric potential is an important concept in electrostatics that helps describe the electrical state of a point in an electric field.
Just as pressure difference causes the flow of fluids, potential difference causes the movement of electric charges.
Electric potential is a scalar quantity and plays a key role in understanding electric fields, capacitors, and electrical circuits.
What is Electric Potential?
Electric potential at a point is defined as the work done in bringing a unit positive test charge from infinity to that point against the electric field.
Mathematically,
Where:
- V = electric potential
- W = work done
- q = charge brought from infinity
Thus, electric potential represents the potential energy possessed by a unit positive charge at a given point.
Physical Meaning of Electric Potential
Electric potential indicates how much work is required to move a positive charge to a particular location in an electric field.
A point with higher potential possesses greater electrical potential energy per unit charge.
A point with lower potential possesses less electrical potential energy per unit charge.
SI Unit of Electric Potential
From the definition:
The SI unit of work is joule (J) and the SI unit of charge is coulomb (C).
Therefore,
Thus, the SI unit of electric potential is volt (V).
Electric Potential Due to a Point Charge
Consider a point charge Q.
The electric potential at a distance r from the charge is:
Where:
- Q = source charge
- r = distance from the charge
- k = Coulomb’s constant
Sign of Electric Potential
The sign of electric potential depends on the nature of the charge producing the field.
Positive Charge
For a positive charge:
The electric potential is positive.
Negative Charge
For a negative charge:
Or,
Where:
- VA = potential at point A
- VB = potential at point B
Meaning of One Volt
One volt is the potential difference between two points when one joule of work is required to move one coulomb of charge between them.
Potential Difference and Work Done
The work done in moving a charge q through a potential difference V is:
This relation is widely used in electrostatics and electrical circuits.
Electric Potential Energy
The electric potential energy of a charge placed in an electric field is:
Where:
- U = electric potential energy
- q = charge
- V = electric potential
Electric potential energy is measured in joules.
Relation Between Electric Field and Potential
Electric field points in the direction of decreasing potential.
The relationship between electric field and potential is:
The negative sign indicates that electric potential decreases in the direction of the electric field.
Potential Due to Multiple Charges
Since electric potential is a scalar quantity, the resultant potential at a point is the algebraic sum of individual potentials.
For several charges:
Or,
This principle is known as the principle of superposition for electric potential.
Equipotential Surfaces
An equipotential surface is a surface on which every point has the same electric potential.
No work is required to move a charge along an equipotential surface.
Electric field lines are always perpendicular to equipotential surfaces.
Solved Example 1
Find the electric potential at a point 0.2 m away from a charge of 4 μC.
Given:
Using:
Substituting values:
Hence,
Solved Example 2
A charge of 2 C is moved through a potential difference of 10 V.
Find the work done.
Given:
Using:
Substituting values:
Therefore,
Difference Between Electric Potential and Potential Difference
| Electric Potential | Potential Difference |
|---|---|
| Potential at a single point. | Difference in potential between two points. |
| Measured relative to infinity. | Measured between two locations. |
| Represents potential energy per unit charge. | Represents work done per unit charge between points. |
Important Points to Remember
- Electric potential is work done per unit charge.
- Potential difference is the work done per unit charge between two points.
- Electric potential is a scalar quantity.
- The SI unit of electric potential is volt (V).
- Potential due to a point charge is V = kQ/r.
- Work done is given by W = qV.
- Potential decreases in the direction of the electric field.
- No work is done while moving a charge along an equipotential surface.
Frequently Asked Questions
What is electric potential?
Electric potential is the work done in bringing a unit positive charge from infinity to a point in an electric field.
What is the SI unit of electric potential?
The SI unit of electric potential is volt (V).
Is electric potential a scalar or vector quantity?
Electric potential is a scalar quantity.
What is potential difference?
Potential difference is the work done per unit charge in moving a charge between two points.
What is the potential due to a point charge?
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