1 / 11

Fields and Waves

Fields and Waves. Lesson 3.6. ELECTROSTATICS - Numerical Simulation. Direct Computation of V. If we can express entire problem in terms of V then:. we can solve directly for V derive all other quantities e.g. E-field, D-field, C and r.

wmulder
Download Presentation

Fields and Waves

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. Fields and Waves Lesson 3.6 ELECTROSTATICS - Numerical Simulation Darryl Michael/GE CRD

  2. Direct Computation of V If we can express entire problem in terms of V then: • we can solve directly for V • derive all other quantities e.g. E-field, D-field, C and r This approach can be used if conductor defines Outer Boundary • can be SYMMETRIC or NON-SYMMETRIC systems Why is this a useful approach?? • V is a scalar field - easier to manipulate than E-field • We can control V on conductors • Can apply numerical methods to solve problem

  3. Use of Laplace and Poisson’s Equations Start with 2 of MAXWELL’s equations: & In rectangular coordinates:

  4. Use of Laplace and Poisson’s Equations Poisson’s equation: Laplace’s equation: (when r = 0) Do Problem 1

  5. h h Numerical Solution: Finite Difference Method Use the FINITE DIFFERENCE Technique for solving problems Solve for approximate V on the Grid - for 2-D Problem Vtop Vright Vcenter Vleft Vcenter at (x,y) = (0,0) Vbottom

  6. h h Vleft Vcenter Vbottom Numerical Solution: Finite Difference Method At (x,y) = (h/2,0) Vtop Vright At (x,y) = (-h/2,0)

  7. Numerical Solution: Finite Difference Method 0 Now, Can get similar expression for

  8. Numerical Solution: Finite Difference Method Finally we obtain the following expression: Rearrange the equation to solve for Vcenter : Poisson Equation Solver Laplace Equation Solver

  9. 100V 10V 30V 60V Numerical Solution: Example Solution Technique - by Iteration Guess a solution : V=0 everywhere except boundaries V1 V2 V4 V3 V1= V2 = V3 = V4 = 0 Put new values back Start:

  10. Numerical Solution - use of EXCEL Spreadsheet Do Problem 2 • To get an accurate solution, need lots of points - one way is to use a SPREADSHEET In spreadsheet, A1 A1 to A31 set boundary voltage = 0Volts Set these cells to 100 Copy B2 formula to rest of cells A31

  11. Numerical Solution: Problems Do Problem 3a and 3b Helpful Hints for Problems 3c - 3e 3c. At point P, what is rs ? Get rs from Boundary Conditions: Approximate 3d. Use spreadsheet to add columns: 3e. Use C=Q/V

More Related