Electric Potential Energy of a System of Charges
Suppose a system of charges q1, q2,…, qn with position vectors r1, r2,…, rn relative to some origin. The potential V1 at P due to the charge q1 can be expressed as
[Tex]V_1=\frac{1}{4\pi\epsilon_0}\frac{q_1}{r_{1P}}[/Tex]
Where r1P is the distance between q1 and P.
Similarly, the potential V2 at P due to q2 and V3 due to q3 can be written as,
[Tex]V_2=\frac{1}{4\pi\epsilon_0}\frac{q_2}{r_{2P}}\\ V_3=\frac{1}{4\pi\epsilon_0}\frac{q_3}{r_{3P}}[/Tex]
where r2P and r3P are the distances of P from charges q2 and q3, respectively, and so on for the potential due to other charges.
By the superposition principle, the potential V at P due to the total charge configuration is the algebraic sum of the potentials due to the individual charge, that is,
V = V1 + V2 + V3 +…. + Vn
The above expression can be expressed as,
[Tex]V=\frac{1}{4\pi\epsilon_0}\frac{q_1}{r_{1P}}+\frac{1}{4\pi\epsilon_0}\frac{q_2}{r_{2P}}+ \frac{1}{4\pi\epsilon_0}\frac{q_3}{r_{3P}}+…..+\frac{1}{4\pi\epsilon_0}\frac{q_n}{r_{nP}}[/Tex]
[Tex]V=\frac{1}{4\pi\epsilon_0}\left(\frac{q_1}{r_{1P}}+\frac{q_2}{r_{2P}}+\frac{q_3}{r_{3P}}+…+\frac{q_n}{r_{nP}}\right)[/Tex]
It is necessary to divide a continuous charge distribution with a charge density (r) into small volume elements of size ∆v, each carrying a charge ρ∆v. Then, for each volume element, compute the potential and add (or, more properly, integrate) all of these contributions to get the overall potential owing to the distribution.
Electric Potential Energy
Electrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.
Sometimes electrical potential energy is confused with electric potential, however, the electric potential at a specific point in an electric field is the amount of work required to transport a unit charge from a reference point to that specific point and electrical potential energy is the amount of energy required to move a charge against the electric field.
In this article, let’s understand the electrical potential energy, electric potential, their key concepts, applications, and solved problems.
Table of Content
- What is Electric Potential Energy?
- Electric Potential Energy Formula
- Electric Potential Energy of a Point Charge
- Electric Potential Energy of a System of Charges
- What is Electric Potential?
- What is Electric Potential Difference?
- Electric Potential Derivation
- Electric Potential of a Point Charge
- Solved Examples on Electric Potential Energy
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