Potential Difference

Potential difference, or voltage, is the difference in electric potential energy between two points. It is denoted by ∆V and has units of volts, or joules per Coulomb.

Voltage denotes the work per unit charge that must be done against a static electric field to move a charge from one point to another. It may represent a source of energy, or lost, stored or used energy. Voltage also is defined such that negative charges are pulled towards higher voltages, while positive charges move towards lower voltages. Thus, current in wires flows from higher to lower voltages.

Potential difference is independent of path taken from one point to another, and may be measured by any of a number of instruments. These include the voltmeter, the potentiometer, and the oscilloscope. It is most typically measured in circuits, and in such situations can be calculated using Ohm ‘s Law, which will be covered in a later atom.

Potential difference in a static field: When a charge q moves from point A to point B, the potential difference is independent of path taken.

Energy Conservation

Energy is conserved in the movement of a charged particle through an electric field, as it is in every other physical situation.

Energy is conserved in the movement of a charged particle through an electric field, as it is in every other physical situation. This phenomenon can be expressed as the equality of summed kinetic (E_kin) and electric potential (E_el) energies:

[latex](\text{E}_{\text{kin}}+\text{E}_{\text{el}})_{\text{initial}}=(\text{E}_{\text{kin}}+\text{E}_{\text{el}})_{\text{final}}[/latex]

Given a stationary test charge in a certain location, an applied electric field will cause the charge to move to one end or the other, depending on the charge (positive test charges will move in the direction of the field; negative charges will move in the opposite direction). In all cases, a charge will naturally move from an area of higher potential energy to an area of lower potential energy.

At the instant at which the field is applied, the motionless test charge has 0 kinetic energy, and its electric potential energy is at a maximum. After that moment, the charge accelerates, and its kinetic energy (from motion) increases as its potential energy decreases. Throughout this time, the sum of potential and kinetic energies remains constant.

Another way to express the previous equation is:

[latex](\frac {1}{2}\text{mv}^2+\text{U})_{\text{initial}}=(\frac {1}{2}\text{mv}^2+\text{U})_{\text{final}}[/latex]

where m and v are the mass and velocity of the electron, respectively, and U is the electric potential energy. U can be calculated as follows:

[latex]\text{U}=\text{q}_0\text{V}=\text{k} \frac{\text{q}_0\text{q}}{\text{r}}[/latex]

where V is the potential difference, k is a constant, q₀ is a test charge, q is another charge, and r is the distance between the charges.

The terms involved in the formula for conservation of energy can be rewritten in many ways, but all expressions are based on the simple premise of equating the initial and final sums of kinetic and potential energy.

Similarities Between Activity of Gravitational and Electric Fields on an Object: The charge, +q, is moved down the electric field in the same way that the object, m, is moved down the hill. In both instances, the particle in motion goes from a higher to a lower potential energy state.

The Electron-Volt

The electron volt is a unit of energy useful in the physics of elementary charges and electricity.

Overview

The electron volt, symbolized as eV and sometimes written as electronvolt, is a unit of energy useful in the physics of elementary charges and electricity.

The electron volt is defined as the amount of energy gained or lost by the charge of an electron moved across a one-volt electric potential difference. As such, it is equal to the product of one volt (1 J/C) and one elementary charge, giving it a value in joules approximately equal to 1.602×10^-19 J.

Not an SI unit in itself, the electron volt became useful through experimentation. Scientists working with electrostatic particle accelerators commonly used the relationship between energy (E), charge (q), and potential difference (V) in their work:

[latex]\text{E}=\text{qV}[/latex]

All calculations of energy from the above equation were quantized as multiples of the elementary charge, q, for a given voltage, and thus arose the common usage of the electron volt as a unit of measurement.

Momentum

Both electron volts and momentum are measures of energy, and the two are related in high-energy physics. Applying a potential difference to an electron gives it energy, which manifests itself in motion of the electron through it. Given that the electron has both mass and velocity, it has momentum. Dividing electron volts by a constant with units of velocity results in a momentum.

Mass

Given that mass is equivalent to energy, the electron volt can measure mass. In particle physics, the equation E=mc² can be rearranged to solve for mass:

[latex]\text{m}=\frac {\text{E}}{\text{c}^2}[/latex]

Wavelength

The energy E, frequency v, and wavelength λ of a photon are related by

[latex]\text{E} (\text{eV}) = \text{hv} = \frac{\text{hc}}{\lambda }[/latex]

where h is the Planck constant and c is the speed of light. Thus, a photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm, and so on.

Energy of Photons in the Visible Spectrum: Relationship between wavelength and energy expressed in electron volts.

Temperature

In plasma physics, the electron volt can be used as a unit of temperature. To convert to Kelvins, simply divide the value of 1 eV (in Joules) by the Boltzmann constant (1.3806505(24)×10^-23 J/K).