College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
Electrostatic potential energy is the potential energy possessed by an electric charge due to its position within an electric field. It is the work done by an external force in bringing a charge from infinity to a specific location in the electric field.
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Electrostatic potential energy is directly proportional to the magnitude of the electric charge and the electric potential at that point.
The electrostatic potential energy of a point charge in an electric field is given by the formula: $U = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}$, where $q_1$ and $q_2$ are the charges, $r$ is the distance between them, and $\epsilon_0$ is the permittivity of free space.
The change in electrostatic potential energy between two points in an electric field is equal to the work done by an external force in moving a charge between those points.
In a capacitor, the energy stored is equal to the electrostatic potential energy of the charges on the capacitor plates, given by the formula: $U = \frac{1}{2}CV^2$, where $C$ is the capacitance and $V$ is the voltage across the capacitor.
Electrostatic potential energy is a scalar quantity, meaning it has magnitude but no direction, unlike electric field or electric force, which are vector quantities.
Review Questions
Explain how electrostatic potential energy is related to the concept of electric potential and potential difference.
Electrostatic potential energy is directly proportional to the electric potential at a given point in an electric field. The change in electrostatic potential energy between two points is equal to the work done by an external force in moving a charge between those points, which is also equal to the potential difference between the two points. Therefore, electrostatic potential energy, electric potential, and potential difference are closely linked concepts that describe the energy and potential associated with electric charges in an electric field.
Describe how the energy stored in a capacitor is related to the concept of electrostatic potential energy.
The energy stored in a capacitor is equal to the electrostatic potential energy of the charges on the capacitor plates. This is given by the formula $U = \frac{1}{2}CV^2$, where $C$ is the capacitance and $V$ is the voltage across the capacitor. The capacitance determines the amount of charge that can be stored on the plates, and the voltage represents the potential difference between the plates. Therefore, the energy stored in a capacitor is directly related to the electrostatic potential energy of the charges on the plates, which is a function of both the charge and the electric potential.
Analyze how the formula for electrostatic potential energy, $U = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}$, demonstrates the relationship between charge, distance, and the energy of an electric field.
The formula for electrostatic potential energy, $U = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}$, shows that the potential energy is directly proportional to the magnitudes of the two charges ($q_1$ and $q_2$) and inversely proportional to the distance ($r$) between them. This demonstrates that the energy of an electric field is dependent on the charges present and the spatial arrangement of those charges. As the charges move closer together, the potential energy increases, and as they move farther apart, the potential energy decreases. This relationship between charge, distance, and energy is a fundamental principle of electrostatic potential energy and the behavior of electric fields.