MIT6_641s09_sol_quiz2006_1

Hint dz 1 z 1 2 1 d z dd z d 2 tan1 3 z dz solution

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Unformatted text preview: : How long do es it take the charge to reach the z = 0 ground plane? Hint: dz 1 z 1 2 − 1 d = − z d(d − z ) + d 2 tan−1 3 z d−z Solution: vz = dz =− dt dz 1 z q2 8 π ε0 m = − 3 11 − z d q2 dt 8 π ε0 m z = −t d−z q2 + 8 π ε0 m ⇒ − 1 d − z d(d − z ) + d 2 tan−1 C constant We use I.C. to find constant ⇒ at t = 0, z (t = 0) = d. ⇒ d 2 tan−1 π 2 3 π3 d = C ⇒ C = d2 0 2 plugging in z = 0 gives the time (T) it takes for the charge to reach the z = 0 ground plane. ⇒ 0 + d 2 tan−1 0 3 0 =− d q2 π3 T + d2 8 π ε0 m 2 2 Spring 2006 Quiz 1 π3 2 2d q2 8π ε0 m 6.641, Spring 2005 ⇒T = = π 2 3 8 π ε0 m d ⇒...
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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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