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Electric Potential Due to a Point Charge
The electric potential at distance `r` from an isolated point charge `Q`, taking zero potential at infinity, is:
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Electric Potential Due to a Point Charge
A charge creates an electric “potential landscape” around itself.
Near a positive charge, potential is more positive.
Farther away, the potential approaches zero.
Recommended for Class 12
Electric Potential Due to a Point Charge
Definition
The electric potential at distance `r` from an isolated point charge `Q`, taking zero potential at infinity, is:
**V = kQ/r**
where:
**k = 14πε₀**
Sign
The electric field of a point charge is:
**E = kQ/r²**
Potential is obtained by considering work per unit charge from infinity to the point.
The result is:
**V = kQ/r**
If:
`Q > 0`
then:
V > 0
relative to infinity.
If:
`Q < 0`
then:
V < 0
Distance Dependence
Potential decreases as:
**1r**
This is different from electric-field strength:
**E ∝ 1r²**
Potential Energy Between Two Point Charges
If another charge `q` is placed at distance `r`:
**U = qV**
Therefore:
**U = kQq/r**
Formula / Key Relation
**V=kQ/r**
**U=kQq/r**
**k≈8.99×10⁹ N m² C⁻²**
Electric Potential Due to a Point Charge — Advanced
The Coulomb potential is the scalar potential associated with the inverse-square electric field:
**V(r)=Q4πε₀r**.
Common Mistakes
Common Mistakes
- Mistake
Do not write:
- Mistake
`V=kQ/r²`
- Mistake
That is not point-charge potential.
- Mistake
Do not ignore the sign of `Q`.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Potential decreases inversely with distance.
For an isolated point charge `Q`, with potential zero at infinity, electric potential at distance `r` is `V=kQ/r`. Its sign follows the sign of the source charge. Potential falls as `1r`, whereas electric-field magnitude falls as `1r²`. A second charge `q` placed there has potential energy `U=kQq/r`.
- Definition
- For an isolated point charge `Q`, with potential zero at infinity, electric potential at distance `r` is `V=kQ/r`. Its sign follows the sign of the source charge. Potential falls as `1r`, whereas electric-field magnitude falls as `1r²`. A second charge `q` placed there has potential energy `U=kQq/r`.
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Practice
PQ
Q1. State point-charge potential formula
PQ
Q2. How does V depend on r?
PQ
Q3. What is V if Q is negative?
PQ
Q4. State potential-energy formula for two charges
PQ
Q5. If distance doubles, what happens to V?
Exam Practice
EQ
Q1. Derive/state electric potential due to a point charge
EQ
Q2. Explain the sign of point-charge potential
EQ
Q3. Compare distance dependence of E and V
EQ
Q4. Derive potential energy between two charges
EQ
Q5. Solve a point-charge potential numerical
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.