Gauge Freedom of Magnetic Potential in Electrodynamics

AI Thread Summary
In electrodynamics, gauge freedom of magnetic potential allows for different choices of gauge, such as the Coulomb and Lorentz gauges, depending on the physical situation. The Coulomb gauge is particularly useful in scenarios without changing electric fields, while the Lorentz gauge applies in covariant theories. Despite the apparent restrictions based on the physics involved, the choice of gauge can simplify mathematical calculations. Ultimately, all gauges describe the same physical phenomena, as Maxwell's equations remain unaffected by these choices. The discussion highlights the importance of selecting the most convenient gauge for the problem at hand.
touqra
Messages
284
Reaction score
0
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.
 
Physics news on Phys.org
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".
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »
Thread 'Recovering Hamilton's Equations from Poisson brackets'

Thread 'Recovering Hamilton's Equations from Poisson brackets'

The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing. The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##. But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
View full post »

Similar threads

I Gauss' law seems to imply instantaneous electric field propagation
Replies
23
Views
575
I Where did I make a mistake in simplifications of equations of EM field?
Replies
1
Views
930
Measuring Electric & Magnetic Fields: Uncovering the Mystery of Gauge Potential
Replies
2
Views
2K
I Magnetic field when the area of the plates of a capacitor increases
Replies
7
Views
1K
I 4-Current vector potential transformation under Gauge fixing
Replies
5
Views
1K
A Electric and magnetic field lines in a plane wave of finite extent
Replies
1
Views
1K
Potential difference defined in non-conservative electric field
Replies
12
Views
1K
I The far reaching ramifications of the work-energy theorem
Replies
31
Views
3K
A Orthogonality of variations in Faddev-Popov method for path integral
Replies
1
Views
1K
I Problem about the usage of Gauss' law involving the curl of a B field
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top