{ Electrostatic Potential Energy David Like

 Overview of the problem  Refresher of useful equations  Problem  Questions Outline

 To estimate the energy involved in a shockwave similar to that which I reported on, consider a 2D square array of identically charged objects (charge q) with regular spacing of d. To make this tractable, consider a small segment of such an array (3X3), centered on the origin. Prompt

Useful Equations Given: Q=q and spacing between 2 dots is d

 What is the electrostatic potential energy of this arrangement (in terms of q and d)? Part A

 3 parts:  Center  Corners (4)  Between Corners (4) Electrostatic Potential Energy

Center Potential Energy Nm J

Corner Potential Energy

Corner Potential Energy Cont’d

Between Potential Energy

Between Potential Energy Cont’d

Total Electrostatic Potential Energy

 What is the electrostatic potential energy per unit area for this arrangement (again in terms of q and d)? Part B

 How much does the electrostatic energy per area change when the spacing is changed from d to d(1+δd)? Part C

 Is it dangerous to scale things in the way suggested for a long-range force like the coulomb force. Nonetheless, given the typical spacing and change in space in the shockwave in the microgravity paper I reported on, provide a numerical estimate of the total energy associated with the shock wave, compared to the unshocked lattice. Part D

Conceptual Answer

Numerical Answer Unshocked Lattice Shocked Lattice VS.

 In the conceptual answer we determined that the unshocked lattice should have higher energy due to the particles being close and we found that it was indeed higher it was higher by a large degree of energy per unit area for such a small change in distance. Does it match?

Questions???

 Samsonov, D. "Shock Melting of a Two- Dimensional Complex (Dusty) Plasma." The American Physical Society (2004): n. pag. Print.  astr.gsu.edu/hbase/electric/elepe.html Sources: