1 / 4

Example: Separation of variables in spherical coordinates

Example: Separation of variables in spherical coordinates. A specified charge density s 0 (q) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere. z. s 0 (q). q. region 2. region 1.

robbiek
Download Presentation

Example: Separation of variables in spherical coordinates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Example: Separation of variables in spherical coordinates A specified charge density s0(q) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere. z s0(q) q region 2 region 1 Since the potential is continuous ar r=R:

  2. Now, let us multiply both sides by Pl(cosq) and utilize the relation: where

  3. Let us consider the distribution: This yields The potential inside the sphere (region 1) is: while the potential outside the sphere (region 2) is: Example: A spherical surface of radius R has the charge uniformly distributed over its surface with a density Q/4pR2, except for a spherical cap at the north pole, defined by the cone q=a. . Find the resulting potential inside and outside the sphere. Hint: use the identity Remember:

  4. Dipole Moment +q -q For dipole moment

More Related