Electric Potential Physics Lesson 24 by Owen Borville 12.23.2025
Electric potential is potential energy per unit charge (V=U/q). The work done to move a charge from point A to B in an electric field is path independent and the work around a closed path is zero. Therefore, the electric field and electric force are conservative. A conservative electric force in an electric field does work that depends only on the start and end points and not the path taken, with no work done over the path. Being conservative allows associating electric potential energy with force and energy is not lost but conserved. V = U/q = -∫(RP)E*dl
Electric potential energy between point charges is U(r) = ke*qQ/r, with the zero reference at infinity. The superposition principle holds for electric potential energy. The potential energy of a system of multiple charges is the sum of the potential energies of the individual pairs.
Potential difference between points A and B, VB-VA, is the change in potential energy of a charge q moved from A to B, and is equal to the change in potential energy divided by the charge. Potential difference is commonly called voltage, and represented by the symbol ΔV = ΔPE (or ΔU)/q and ΔPE (or ΔU) = qΔV.
Potential difference between two points: ΔVAB = VB-VA = -∫(AB)E*dl
An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1V. 1eV = (1.60 x 10^-19 C) (1 V) = (1.60 x 10^-19 C)(1 J/C) = 1.60 x 10^-19 J
Mechanical energy is the sum of the kinetic and potential energy of the system (KE + PE), and this sum is a constant.
The voltage between points A and B is VAB = Ed and E = VAB/d (with uniform E - field only) (d is the distance from A to B between the plates).
The voltage and electric field relationship is E = -ΔV/ Δs (Δs is the distance over which the change in potential ΔV takes place. The minus sign signifies that E points in the direction of decreasing potential). The electric field is known as the gradient of slope of the electric potential. E = -∇ V
The electric potential of a point charge is V = kQ/r. Electric potential is a scalar quantity, and electric field is a vector quantity with magnitude and direction. Addition of voltages as numbers gives the voltage due to a combination of point charges, allowing the use of the principle of superposition: Vp = ke ∑qi/ri (N=1) whereas addition of individual fields as vectors gives the total electric field. An electric dipole contains two equal and opposite charges a fixed distance apart, with a dipole moment p = qd. Continuous charge distributions can be calculated with VP = ke ∫dq/r.
Electric potential due to a dipole = Vp = ke*p*r/r^2
Just as electric potential is calculated by integrating over the electric field, the derivative of the electric potential can be taken to calculate the electric field. These calculations can be done for individual components of the electric field, or the entire electric field vector can be calculated with the gradient operator. In three dimensions, partial derivatives are used to calculate electric field components for each dimension in x, y, and z vector components.
Equipotential lines are lines along which the electric potential is constant in two dimensions. An equipotential surface is a three-dimensional version of equipotential lines, where the collection of points in space are all at the same potential. Equipotential surfaces are always perpendicular to electric field lines. The process by which a conductor can be fixed a zero volts by connecting it to the earth with a good conductor is called grounding. Conductors in static equilibrium are equipotential surfaces. Topographic maps use a similar concept to show elevation changes as gravitational equipotential lines show changes in electric potential.
Electrostatics is the study of electric fields in static equilibrium. Research is done using a Van de Graaff generator and many practical applications have been developed, including photocopiers, laser printers, ink jet printers, and electrostatic air filters.
Electric potential is potential energy per unit charge (V=U/q). The work done to move a charge from point A to B in an electric field is path independent and the work around a closed path is zero. Therefore, the electric field and electric force are conservative. A conservative electric force in an electric field does work that depends only on the start and end points and not the path taken, with no work done over the path. Being conservative allows associating electric potential energy with force and energy is not lost but conserved. V = U/q = -∫(RP)E*dl
Electric potential energy between point charges is U(r) = ke*qQ/r, with the zero reference at infinity. The superposition principle holds for electric potential energy. The potential energy of a system of multiple charges is the sum of the potential energies of the individual pairs.
Potential difference between points A and B, VB-VA, is the change in potential energy of a charge q moved from A to B, and is equal to the change in potential energy divided by the charge. Potential difference is commonly called voltage, and represented by the symbol ΔV = ΔPE (or ΔU)/q and ΔPE (or ΔU) = qΔV.
Potential difference between two points: ΔVAB = VB-VA = -∫(AB)E*dl
An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1V. 1eV = (1.60 x 10^-19 C) (1 V) = (1.60 x 10^-19 C)(1 J/C) = 1.60 x 10^-19 J
Mechanical energy is the sum of the kinetic and potential energy of the system (KE + PE), and this sum is a constant.
The voltage between points A and B is VAB = Ed and E = VAB/d (with uniform E - field only) (d is the distance from A to B between the plates).
The voltage and electric field relationship is E = -ΔV/ Δs (Δs is the distance over which the change in potential ΔV takes place. The minus sign signifies that E points in the direction of decreasing potential). The electric field is known as the gradient of slope of the electric potential. E = -∇ V
The electric potential of a point charge is V = kQ/r. Electric potential is a scalar quantity, and electric field is a vector quantity with magnitude and direction. Addition of voltages as numbers gives the voltage due to a combination of point charges, allowing the use of the principle of superposition: Vp = ke ∑qi/ri (N=1) whereas addition of individual fields as vectors gives the total electric field. An electric dipole contains two equal and opposite charges a fixed distance apart, with a dipole moment p = qd. Continuous charge distributions can be calculated with VP = ke ∫dq/r.
Electric potential due to a dipole = Vp = ke*p*r/r^2
Just as electric potential is calculated by integrating over the electric field, the derivative of the electric potential can be taken to calculate the electric field. These calculations can be done for individual components of the electric field, or the entire electric field vector can be calculated with the gradient operator. In three dimensions, partial derivatives are used to calculate electric field components for each dimension in x, y, and z vector components.
Equipotential lines are lines along which the electric potential is constant in two dimensions. An equipotential surface is a three-dimensional version of equipotential lines, where the collection of points in space are all at the same potential. Equipotential surfaces are always perpendicular to electric field lines. The process by which a conductor can be fixed a zero volts by connecting it to the earth with a good conductor is called grounding. Conductors in static equilibrium are equipotential surfaces. Topographic maps use a similar concept to show elevation changes as gravitational equipotential lines show changes in electric potential.
Electrostatics is the study of electric fields in static equilibrium. Research is done using a Van de Graaff generator and many practical applications have been developed, including photocopiers, laser printers, ink jet printers, and electrostatic air filters.