I am having trouble understanding how to find symmetries given a

  • Thread starter berra
  • Start date
  • Tags
    Symmetries
In summary, the conversation discusses how to find symmetries in a problem involving a cylinder conductor in electrostatics. The reasoning is to assume a homogenous charge distribution and observe the E-field for translations in z and phi. One approach is to use the divergence and curl, but there are still components that need to be accounted for. Another suggestion is to use Faraday's law and assume that Ez and Ephi are trivial solutions to the PDE. It is also mentioned that the potential is not dependent on z or phi, which means those components of E will vanish. The possibility of using symmetry groups is also brought up, but the participants are unsure about its applicability.
  • #1
berra
21
0
I am having trouble understanding how to find symmetries given a problem.
Ex:
Cylinder, infinite in z, that is a conductor in electrostatics.
My reasoning is: assuming a homogenous charge distribution, the E-field should be symmetric for translations in z and phi so those derivatives are zero. But how do I do for the components? My only guess was to take the divergence and curl and use helmholtz theorem, but in the curl I still have dEz/drho and an Ephi term. Is the convention to use faradays law and assuming Ez and Ephi are the trivial solutions to the PDE so the Efield only has a rho component?
 
Physics news on Phys.org
  • #2


Can't you argue that since the potential is not dependent on z or phi, the z and phi components of E vanish?
 
  • #3


Ah yes! That would take care of it! Nice. Is there any other more general approach? Like symmetry groups somehow?
 
  • #4


I don't really know enough about symmetry groups in this context to answer that. Hopefully someone more knowledgeable will drop by!
 
  • #5


Okay, thanks for your answer!
 

FAQ: I am having trouble understanding how to find symmetries given a

How do I identify symmetries in a given shape or object?

To identify symmetries, look for patterns of repetition or reflection in the shape or object. These patterns can be vertical, horizontal, or rotational. You can also use a mirror or tracing paper to help visualize the symmetries.

Can you explain the difference between line and rotational symmetries?

Line symmetries refer to the reflection of a shape or object across a line, while rotational symmetries refer to the rotation of a shape or object around a central point. Line symmetries are typically easier to identify than rotational symmetries.

How many symmetries can a shape or object have?

The number of symmetries a shape or object can have depends on its complexity. Simple shapes like squares and circles can have multiple symmetries, while more complex shapes may have fewer or none at all.

Are symmetries important in science?

Symmetries play a crucial role in science, particularly in fields like physics and chemistry. They help us understand the structure and behavior of molecules, crystals, and other natural phenomena.

Is there a formula or method for finding symmetries?

There is no specific formula or method for finding symmetries, as it largely relies on observation and visual analysis. However, there are some mathematical principles that can be applied, such as the concept of congruence and properties of shapes and angles.

Similar threads

I How to use geometrical symmetries -- general advice? (Vector potential)
Replies
2
Views
1K
How Do You Prove Symmetry Arguments in E&M?
Replies
4
Views
2K
I Maxwell's equations PDE interdependence and solutions
Replies
5
Views
845
Having trouble understanding "Faraday cage"
Replies
3
Views
1K
I Finding the weak form of an eq. with DG elements (finite elements)
Replies
6
Views
3K
Electrostatics - method of conformal mapping (from Landau)
Replies
1
Views
2K
How Do Symmetry Considerations Affect the Electric Field in a Dielectric Plate?
Replies
4
Views
3K
BRS: The Weyl Vacuums. I. Definition, Geometrical Properties, Symmetries
Replies
11
Views
2K
How Does Spontaneous Symmetry Breaking Explain Particle Masses?
Replies
2
Views
3K
I Atmospheric Density vs Altitude in an O'Neil Cylinder
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top