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Potential Due to Multiple Charges and Equipotential Surfaces
Because electric potential is scalar, the total potential produced by several point charges is the algebraic sum of their individual potentials.
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Potential Due to Multiple Charges and Equipotential Surfaces
Potential is easier to add than force because it has no direction.
Just calculate each charge's potential, keep its sign, and add the numbers.
An equipotential surface is like an electrical “same-height contour.”
Recommended for Class 12
Potential Due to Multiple Charges and Equipotential Surfaces
Definition
Because electric potential is scalar, the total potential produced by several point charges is the algebraic sum of their individual potentials.
An equipotential surface is a surface on which electric potential has the same value everywhere.
Equipotential Surface
For charges:
`Q₁, Q₂, ... Qn`
at distances:
`r₁, r₂, ... rn`
the total potential is:
**V = kΣ(Qᵢ/rᵢ)**
This is scalar superposition.
If two points are on the same equipotential:
**ΔV = 0**
Therefore:
**ΔU=qΔV=0**
and the electrostatic field does no net work moving a charge along that equipotential path.
Relation to Electric Field
Electric field is perpendicular to equipotential surfaces.
If it had a component along an equipotential surface, it would change the potential along that surface.
Point Charge
Equipotential surfaces around an isolated point charge are spherical surfaces centered on the charge.
Formula / Key Relation
**Vtotal = ΣVᵢ**
**V = kΣ(Qᵢ/rᵢ)**
On equipotential:
**ΔV=0**
Potential Due to Multiple Charges and Equipotential Surfaces — Advanced
Potential obeys scalar superposition, while:
**E = −∇V**
shows that the field points normal to surfaces of constant potential toward decreasing V.
Common Mistakes
Common Mistakes
- Mistake
Do not add the magnitudes only. Negative source charges contribute negative potential.
- Mistake
Do not add electric potential using vector components.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Potentials add algebraically; field lines cross equipotentials at right angles.
The total electric potential from multiple point charges is the scalar sum `V=kΣ(Qᵢ/rᵢ)`. Signs of the source charges must be retained. An equipotential surface has the same V everywhere, so moving a charge along it gives `ΔV=0` and no change in electrostatic potential energy. Electric-field lines are perpendicular to equipotential surfaces and point toward decreasing potential.
- Definition
- The total electric potential from multiple point charges is the scalar sum `V=kΣ(Qᵢ/rᵢ)`. Signs of the source charges must be retained. An equipotential surface has the same V everywhere, so moving a charge along it gives `ΔV=0` and no change in electrostatic potential energy. Electric-field lines are perpendicular to equipotential surfaces and point toward decreasing potential.
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Practice
PQ
Q1. How are potentials combined?
PQ
Q2. Define equipotential surface
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Q3. What is work along an equipotential?
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Q4. How is E oriented relative to equipotential surfaces?
PQ
Q5. Write total potential formula
Exam Practice
EQ
Q1. Explain superposition of electric potential
EQ
Q2. Define and explain equipotential surfaces
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Q3. Explain the relation between E and equipotentials
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Q4. Calculate potential due to several charges
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Q5. Explain why no electrostatic work is done along an equipotential
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.