MIT6_641s09_sol_quiz2006_1

Solution force ma dv f due to image charge dt dv q q

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Unformatted text preview: ? Solution: Force = ma dv = F due to image charge dt dv q (−q ) q 2 dvz ⇒m = =− i ⇒m 2z dt 4π ε0 (2z ) dt 4π ε0 4z 2 dvz dvz q2 dvz dz dvz d ⇒ =− Use of chain rule: = = vz = dt 1 6 π ε 0 mz 2 dt dz dt dz dz ⇒m 2 vz 2 1 Spring 2006 Quiz 1 d dz 2 vz 2 6.641, Spring 2005 q2 ⇒ 1 6 π ε 0 mz 2 2 vz 2 ⇒ =− d = − q2 dz 1 6 π ε 0 mz 2 q2 +C 8 π ε 0 mz Use I.C. vz (z = d) = 0 2 ⇒ vz = + q ⇒ C = − 8πε0 md 2 vz = 2 q2 8 π ε0 m 11 − z d q2 8π ε0 m 1 z ⇒ vz (z ) = − − 1 d since particle is moving towards the conducting ground plane v = vz iz (vz has minus sign) B Question...
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This note was uploaded on 12/02/2010 for the course ECE 6.641 taught by Professor Zahn during the Spring '09 term at MIT.

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