Electric Potential Energy of a Point Charge
Consider the origin of a point charge Q. Consider Q to be a positive character. We wish to find the electrical potential energy at any location P using the position vector r from the origin. To do so, we need to figure out how much work it takes to transfer a unit-positive test charge from infinity to point P.
When Q > 0, the work done against the repulsive force on the test charge is positive. Because the work is independent of the path, we choose a convenient path, i.e., along the radial direction from infinity to point P.
Work done in bringing a unit positive test charge from infinity to the point P, against the repulsive force of charge Q (Q > 0), is the potential at P due to the charge Q.
The electrostatic force on a unit positive charge at some intermediate point P′ on the path equals to
[Tex]\frac{Q\times1}{4\pi\epsilon_0r’^2}\hat{r’}[/Tex]
where [Tex] \hat{r’} [/Tex] is the unit vector along OP’, therefore, work done against this force from r′ to r′ + ∆r′ can be written as
[Tex]\Delta{W}=-\frac{Q}{4\pi\epsilon_0r’^2}\Delta{r’}[/Tex]
The negative sign represents ∆r′ < 0, and ∆W is positive. Total work done (W) by the external force is determined by integrating the above equation on both sides, from r′ = ∞ to r′ = r,
[Tex]W=-\int_{∞}^{r} \frac{Q}{4\pi\epsilon_0r’^2}d{r’}\\ W=\left[\frac{Q}{4\pi\epsilon_0r’}\right]_∞^r\\ W=\frac{Q}{4\pi\epsilon_0r}[/Tex]
The potential at P due to the charge Q can be expressed as,
[Tex]V(r)=\frac{Q}{4\pi\epsilon_0r}[/Tex]
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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