Potential of Dipole in Cylindrical coordinates

Geocentric
Messages
15
Reaction score
0

Homework Statement


I have been given the problem of finding the potential of a dipole in cylindrical coordinates. The only way that comes to my mind is to extract the dipole term from the multipole expansion of the potential of an arbitrary charge distribution in cylindrical coordinates. But I am not quite sure about it. Can anyone please throw more light on how to go about this problem? Please ignore if I have said something stupid.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
If you're not meant to just take an expression for the dipole potential and just substitute coordinates, then doing the multipole expansion seems like your best bet. With an obvious choice of coordinates, the expansion is fairly easy.
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
View full post »
Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
View full post »

Similar threads

Electrostatic polarization of an axially symmetric conductor
Replies
8
Views
2K
Dipole Moment of a Hollow Sphere, simplify calculation
Replies
1
Views
2K
I Origin of coordinates in multipole expansion
Replies
10
Views
1K
How Does the Nuclear Quadrupole Moment Explain Nucleus Deformation?
Replies
6
Views
2K
Multipole expansion of a line charge distribution
Replies
7
Views
4K
I Question regarding how to interpret dipole moment for bound charges
Replies
1
Views
2K
Potential inside a cylindrical shell with a line charge
Replies
6
Views
4K
Deriving magnetic dipole moment from multipole expansion
Replies
1
Views
3K
Surface bound charge on the outer surface of a dielectric
Replies
1
Views
2K
Maximizing Symmetry in Lagrangian for a Particle in 3D Cylindrical Coordinates
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top