Electric potential is a scalar quantity that represents the work done per unit positive charge in bringing a test charge from infinity to a given point.
One of the most important applications of electric potential is determining the potential produced by a point charge.
The concept is widely used in electrostatics, capacitors, and electric field calculations.
What is a Point Charge?
A point charge is an electric charge whose dimensions are negligible compared to the distances involved in the problem.
Examples include electrons, protons, and small charged particles.
Although real charges occupy some space, they are often treated as point charges for simplicity.
Definition of Electric Potential
Electric potential at a point is defined as the work done in bringing a unit positive charge from infinity to that point against the electric field.
Where:
- V = electric potential
- W = work done
- q = test charge
Derivation of Potential Due to a Point Charge
Consider a point charge Q placed in space.
Let a test charge q be brought from infinity to a point P located at a distance r from the charge.
The electric field due to the charge Q at distance r is:
The small work done in moving the charge through a small distance dr is:
Since:
Therefore,
Substituting the value of E:
The total work done in bringing the charge from infinity to distance r is:
Solving the integration:
Electric potential is:
Therefore,
This is the expression for electric potential due to a point charge.
Alternative Form
Since:
The formula may also be written as:
Factors Affecting Electric Potential
The electric potential depends on:
- Magnitude of charge Q
- Distance r from the charge
- Permittivity of the medium
From the equation:
Potential is directly proportional to charge and inversely proportional to distance.
Sign of Electric Potential
Positive Charge
If the source charge is positive:
Then:
The electric potential is positive everywhere around the charge.
Negative Charge
If the source charge is negative:
If distance is doubled:
If distance is tripled:
At infinity:
This is why infinity is chosen as the reference point for electric potential.
Graph of Potential vs Distance
The graph of electric potential versus distance is a rectangular hyperbola.
As distance increases, potential gradually approaches zero.
The potential never becomes infinite except at the exact location of the point charge.
Potential Due to Multiple Point Charges
Electric potential is a scalar quantity.
Therefore, potentials are added algebraically.
If several charges are present:
Or,
This is known as the principle of superposition for electric potential.
Potential at the Midpoint of Two Equal Charges
Consider two equal positive charges placed symmetrically.
The potential at the midpoint is:
Since potential is scalar, both contributions add directly.
Unlike electric field, potential does not cancel due to opposite directions.
Solved Example 1
Find the electric potential at a point located 0.5 m from a charge of 2 μC.
Given:
Using:
Substituting values:
Therefore,
Solved Example 2
A charge of −5 μC is placed at the origin.
Find the potential at a point 2 m away.
Given:
Using:
Substituting values:
Hence,
Important Points to Remember
- Electric potential due to a point charge is a scalar quantity.
- The formula is V = kQ/r.
- Potential decreases inversely with distance.
- Positive charges produce positive potential.
- Negative charges produce negative potential.
- Potential at infinity is taken as zero.
- Potentials from multiple charges add algebraically.
Frequently Asked Questions
What is the formula for potential due to a point charge?
Is electric potential a scalar quantity?
Yes, electric potential is a scalar quantity.
Why is potential at infinity taken as zero?
Because the electric field becomes negligible at very large distances from the charge.
Can electric potential be negative?
Yes. The potential is negative around a negative charge.
How does potential vary with distance?
The potential decreases as the distance from the charge increases.
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