ECE
MIT6_641s09_sol_quiz2006_1

# MIT6_641s09_sol_quiz2006_1 - MIT OpenCourseWare...

• Notes
• 6

This preview shows pages 1–4. Sign up to view the full content.

MIT OpenCourseWare 6.641 Electromagnetic Fields, Forces, and Motion Spring 2009 For information about citing these materials or our Terms of Use, visit: .

This preview has intentionally blurred sections. Sign up to view the full version.

6.641 — Electromagnetic Fields, Forces, and Motion Spring 2006 Quiz 1 - Solutions Prof. Markus Zahn MIT OpenCourseWare Problem 1 z z z q -q σ = ∞ ε 0 image charge Figure 1: Charge q of a mass m above a perfectly conducting ground plane and its image charge q . (Image by MIT OpenCourseWare.) A Question: What is the velocity of the charge as a function of position z ? Solution: Force = ma dv m dt = F due to image charge dv q ( q ) dv z q 2 m = m = dt 4 πε 0 (2 z ) 2 dt 4 πε 0 4 z 2 dv z q 2 dv z dv z dz dv z d p v 2 P dt = 16 πε 0 mz Use of chain rule: dt = dz dt = dz v z = dz 2 z 2 i z 1
r i R ± ± ² R ± bB³´ R b ´ R ± Spring 2006 Quiz 1 6.641, Spring 2005 d p v z 2 P q 2 i p v z 2 P i q 2 2 2 dz 2 = 16 πε 0 mz d 2 = 16 πε 0 mz dz 2 2 q v = + + C z 8 πε 0 mz Use I.C. v z ( z = d ) = 0 2 8 πε 0 md C = q q 2 p 1 1 P

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Spring '09
• Zahn
• Electromagnet, MIT OpenCourseWare, Electromagnetic field, Pallavolo Modena, Sisley Volley Treviso

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern