# Gauge Freedom of Magnetic Potential in Electrodynamics

• touqra
In summary, the concept of gauge freedom in electrodynamics refers to the ability to choose different gauges, such as the Coulomb or Lorentz gauge, to describe the same physical situation. The choice of gauge is restricted by the physics involved, but the same physics can be described in multiple gauges. The Coulomb gauge is useful for non-covariant theory, while the Lorentz gauge is used for the covariant theory. The fields and equations in electrodynamics are not affected by the choice of gauge.

#### touqra

Hi,

In Electrodynamics, one often state about the gauge freedom of the magnetic potential. And so, we may choose to impose for example the Coulomb gauge, where the divergence of the potential is zero. But, isn't this only true if there exist no changing electrical field,
$\frac{\partial E}{\partial t}$ = 0 as in the magnetostatics case ? Why would it be called a freedom then, if this is situation dependent ?

Thanks.

http://en.wikipedia.org/wiki/Gauge_fixing
Your choice of gauge it is best to fix is restricted by the physics - yep.
However, the physics described in the coulomb gauge may also be described in the lorentz gauge, or some other, so you are free to choose. Best practice is to choose the gauge that makes the math easier.

Simon Bridge said:
http://en.wikipedia.org/wiki/Gauge_fixing
Your choice of gauge it is best to fix is restricted by the physics - yep.
However, the physics described in the coulomb gauge may also be described in the lorentz gauge, or some other, so you are free to choose. Best practice is to choose the gauge that makes the math easier.

Hence, I pointed out there exist no changing electric field or potential. If this is the case, the Lorentz gauge would reduced to the Coulomb gauge. So, essentially, there is only one gauge, i.e. the Lorentz gauge. And this will get reduced to "any" gauge according to the situation. I still don't see why the list of gauges and freedoms to choose from.

The Coulomb gauge is the more useful for the non-covariant theory, having particular advantages for slow-moving particles. Another choice, the Lorentz gauge, is for the covariant theory. The fields, and Maxwell's equations, are unaffected by gauge. This is the main difference.

iirc: there are an arbitrary number of gauges - see the link: it includes a description of what is meant by "gauge freedom".

## 1. What is gauge freedom in electrodynamics?

Gauge freedom, also known as gauge invariance, refers to the property of certain physical theories, such as electrodynamics, that allows for different mathematical descriptions of the same physical system. In the case of electrodynamics, gauge freedom arises from the fact that the electric and magnetic fields can be described using different mathematical equations without changing the physical behavior of the system.

## 2. Why is gauge freedom important in electrodynamics?

Gauge freedom is important in electrodynamics because it allows for a more elegant and concise mathematical formulation of Maxwell's equations, which govern the behavior of electric and magnetic fields. It also allows for a better understanding of the physical principles underlying electromagnetism.

## 3. What is the role of the magnetic potential in gauge freedom?

The magnetic potential is one of the four basic quantities used to describe electromagnetic fields, along with the electric potential, electric field, and magnetic field. In the context of gauge freedom, the magnetic potential plays a crucial role as it is one of the quantities that can be freely chosen without affecting the physical behavior of the system.

## 4. How is gauge freedom related to the choice of gauge in electrodynamics?

Gauge freedom is closely related to the concept of choosing a gauge in electrodynamics. A gauge is a specific mathematical representation of the electric and magnetic fields, and different gauges can be chosen to describe the same physical system. This choice of gauge is closely linked to the gauge freedom in electrodynamics.

## 5. Can gauge freedom be observed in real-world phenomena?

While gauge freedom is a fundamental concept in electrodynamics, it is not directly observable in real-world phenomena. This is because the physical behavior of a system is independent of the specific gauge chosen to describe it. However, the effects of gauge freedom can be seen in the different mathematical formulations and predictions of electromagnetic phenomena based on different gauges.