Definition and Calculation of Electric Potential Energy
– Electric potential energy is the work required to assemble a system of point charges.
– It can also be defined as the total work done by an external agent to bring a charge or system of charges from infinity to its present configuration.
– The electrostatic potential energy of a point charge in the presence of an electric field is defined as the negative of the work done by the electrostatic force.
– It can also be defined as the product of the charge and the electric potential.
– The electric potential energy can be calculated using the formula U_E(r) = -∫qE(r)dr.
– Electric potential energy is the energy stored in a system of charges due to their positions.
– It can be calculated using the formula U_E = (1/2) * ∫ ho * Φ * dV, where U_E is the total electrostatic potential energy, ho is the continuous volume charge, Φ is the electric potential, and integration is done over the entire volume of the dielectric.
– This expression is valid for cases where the smallest increment of charge is zero, such as dielectrics with metallic electrodes or dielectrics containing many charges.
– The factor of one half accounts for the double counting of charge pairs.
– The electric potential energy can also be expressed in terms of the electric displacement field, where U_E = (1/2) * ∫ D * E * dV, with D being the electric displacement field.
Units
– The SI unit of electric potential energy is the joule.
– In the CGS system, the unit of energy is the erg.
– Electronvolts can also be used, where 1 eV = 1.602×10^-19 joules.
Electrostatic Potential Energy of One Point Charge
– The electrostatic potential energy of a point charge in the presence of another point charge is given by U_E(r) = k_e(qQ/r), where k_e is the Coulomb constant, q and Q are the charges, and r is the distance between the charges.
– The electrostatic potential energy is mutually shared by the charges.
– The total stored energy in a system of charges at positions r_1, r_2, …, r_N is U_E = (1/2)∑q_iΦ(r_i), where q_i is the charge and Φ(r_i) is the electric potential at position r_i.
Energy Stored in a System of Point Charges
– The electrostatic potential energy of a system containing only one point charge is zero.
– The interaction of a point charge with its own electrostatic potential does not contribute to the stored energy of the system.
– The electrostatic potential energy of a point charge in the presence of another point charge is given by U_E = (1/4πε_0)(qQ_1/r_1), where ε_0 is the permittivity of free space, q and Q_1 are the charges, and r_1 is the separation between the charges.
– The energy stored in a system of two point charges can be calculated using the formula U_E = (1/2)ε_0|E|^2, where E is the electric field.
– The electric potential energy stored in a capacitor is given by U_E = (1/2)CV^2, where C is the capacitance and V is the electric potential difference.
– The total energy stored in a capacitor can also be expressed as U_E = (1/2)QV, where Q is the charge stored in the capacitor.
– The total energy stored in a few-charge capacitor is U_E = (1/2)Q^2/C, where Q is the total charge on the capacitor and C is the capacitance.
Additional Considerations and Validity
– In certain cases, an additional term must be considered in the expression of electrostatic energy.
– This extra energy arises from the energy transfer between capacitor plates in a virtual experiment.
– While this extra energy cancels for insulators, it cannot be ignored for semiconductors and other materials.
– The energy cancellation for insulators is due to the absence of free charges.
– The presence of this additional energy term affects the calculation of total electrostatic potential energy in dielectrics.
– The reference zero for electric potential energy is often taken to be a state where individual point charges are well separated and at rest.
– The reference state allows for convenient calculations and comparisons.
– The choice of reference zero does not affect the absolute value of electric potential energy.
– Consideration of the separation of charges is crucial in accurately calculating electric potential energy.
– The expressions for electric potential energy in terms of continuous volume charge and electric displacement field are valid for specific scenarios.
– These expressions are applicable when the smallest increment of charge is zero.
– Dielectrics with metallic electrodes or dielectrics containing many charges satisfy this condition.
– The integration in the expressions is done over the entire volume of the dielectric.
– The validity of the expressions relies on the specific conditions and nature of the dielectric material.
References:
– Grant and Phillips’ book ‘Electromagnetism’
– Halliday, Resnick, and Walker’s ‘Fundamentals of Physics’ (5th edition)
– Sallese’s article ‘A new constituent of electrostatic energy in semiconductors’ in The European Physical Journal B Source: https://en.wikipedia.org/wiki/Electric_potential_energy
Electric potential energy is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may be said to have electric potential energy by virtue of either its own electric charge or its relative position to other electrically charged objects.
| Electric potential energy | |
|---|---|
Common symbols | UE |
| SI unit | joule (J) |
Derivations from other quantities | UE = C · V2 / 2 |
The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields.
