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Electric Potential Due To Multiple Charges

Electric Potential Due To Multiple Charges :- Electric potential is a scalar quantity that describes the potential energy per unit charge at a point in an electric field. When dealing with multiple point charges, the total electric potential at a given point in space is the algebraic sum of the potentials due to each individual charge.

Principle of Superposition

(Electric Potential Due To Multiple Charges)

The key concept used in calculating electric potential due to multiple charges is the principle of superposition. According to this principle, the total electric potential at a point (say P) due to several point charges is the sum of the potentials due to each charge taken individually.

Mathematically, for point charges :

$\displaystyle V=\sum\limits_{i=1}^{N}{\frac{k{{q}_{i}}}{{{r}_{i}}}}=\frac{k{{q}_{1}}}{{{r}_{1}}}+\frac{k{{q}_{2}}}{{{r}_{2}}}+\frac{k{{q}_{3}}}{{{r}_{3}}}+.....$ …..(1)

where :

is Coulomb’s constant (,
is the ^th charge,
is the distance from the ^th charge to the point where the potential is being calculated.

If $\displaystyle \overrightarrow{{{r}_{1}}}$ , $\displaystyle \overrightarrow{{{r}_{2}}}$ , $\displaystyle \overrightarrow{{{r}_{3}}}$ , ….. $\displaystyle \overrightarrow{{{r}_{N}}}$ are the position vectors of the charges q₁, q₂, q₃,…..q_N respectively, then electrostatic potential at point P , whose position vector is $\displaystyle \overrightarrow{{{r}_{0}}}$ would be :-

$\displaystyle V=\frac{1}{4\pi {{\varepsilon }_{0}}}\sum\limits_{i=1}^{N}{\frac{{{q}_{i}}}{\left| \overrightarrow{{{r}_{0}}}-\overrightarrow{{{r}_{i}}} \right|}}$ …..(2)

Characteristics of Electric Potential Due To Multiple Charges

Scalar Nature : Unlike electric field vectors, potentials are scalars, so they simply add or subtract based on sign.
Sign Matters : Positive charges contribute positive potential, and negative charges contribute negative potential.

Electric Potential Due To Multiple Charges

Principle of Superposition

(Electric Potential Due To Multiple Charges)

Characteristics of Electric Potential Due To Multiple Charges

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