Definition of electric charge as rationalized charge (2024)

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In summary: The meaning of the term 'rationalized' when referring to 'electron charge' is that the charge is expressed in terms of the natural units of length, mass, and time. In Lorentz-Heaviside units (also called 'rationalized'), Coulomb's law is F = q1q2/(4πr2), and in Gaussian units (also called 'non-rationalized'), Coulomb's law is F = q1q2/r2. Both possibilities are incorporated into different natural unit systems. In natural units, hbar and c are one. The electron charge is dimensionless, and e^2=1/137.036 in gaussian natural units, or e^

  • #1

voltan

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definition of electric charge as "rationalized charge"

Hi All,

I wonder about the meaning of the term "rationalized" when saying "rationalized electron charge." Does this mean that the charge is given in natural units?

Thank you very much!

Best

  • #2

Short answer: sort of.
Natural units would be expected to make the Coulomb constant k=1... which is termed "non-rationalized".

Rationalized charge is given in Lorentz–Heaviside units, which has k=1/ε0... on, making charge units: Coulombs per root-permittivity-of-free-space.

http://en.wikipedia.org/wiki/Natural_units
In the SI unit system, electric charge is a separate fundamental dimension of physical quantity, but in natural unit systems charge is expressed in terms of the mechanical units of mass, length, and time, similarly to cgs. There are two common ways to relate charge to mass, length, and time: In Lorentz–Heaviside units (also called "rationalized"), Coulomb's law is F = q1q2/(4πr2), and in Gaussian units (also called "non-rationalized"), Coulomb's law is F = q1q2/r2.[1] Both possibilities are incorporated into different natural unit systems.

  • #3

Meir Achuz

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voltan said:

I wonder about the meaning of the term "rationalized" when saying "rationalized electron charge." Does this mean that the charge is given in natural units?

'Rationalized' means that q^2 is divided by 4pi wherever it appears. These are also called
'Heaviside units'. This leads to simplification of some equations at the cost of complication of others, and considerable confusion.
In 'Gaussian units q^2 is divided by 1, which is an easier number to memorize.
QEDers are split on which to use, so be careful in reading a QED paper to check which it is.
S.I. units go on to also divide by epsilonzero which complicates all equations.
Fortunately, most QED papers don't use SI.
In natural units, hbar and c are one. The electron charge is dimensionless, and
e^2=1/137.036 in gaussian natural units, or e^2/4pi=1/137.036 in Heaviside natural units.

Related to Definition of electric charge as rationalized charge

1. What is the definition of electric charge as rationalized charge?

The definition of electric charge as rationalized charge is a concept in electromagnetism that represents the fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It is a measure of the amount of electric force that an object experiences due to the presence of other charged objects.

2. Why is it important to rationalize electric charge?

Rationalizing electric charge allows for a consistent and standardized system of measurement. It eliminates the use of arbitrary units and instead uses a base unit, the Coulomb, which is defined in terms of fundamental physical constants. This makes calculations and experiments more accurate and efficient.

3. How is electric charge rationalized?

Electric charge is rationalized by defining the Coulomb constant, also known as the permittivity of free space, as a fixed value. This constant then fixes the value of the elementary charge (e), which is the charge carried by a single proton or electron. By using these defined values, the unit of charge, the Coulomb, can be expressed in terms of fundamental physical constants.

4. What is the difference between rationalized and non-rationalized electric charge?

Rationalized electric charge is expressed in terms of fundamental physical constants, such as the Coulomb constant and the elementary charge, while non-rationalized electric charge is expressed in arbitrary units. Rationalized charge allows for a more accurate and consistent system of measurement, while non-rationalized charge may vary depending on the unit used.

5. How does rationalizing electric charge affect the equations of electromagnetism?

Rationalizing electric charge does not change the fundamental equations of electromagnetism, such as Coulomb's law or Gauss's law. However, it simplifies the equations and makes them easier to work with by eliminating the need for conversion factors. It also helps to maintain the symmetry and beauty of these equations, which are fundamental principles in physics.

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