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# tsl331 - Intermediate Exam I Problem#1(Spring'05 The...

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Intermediate Exam I: Problem #1 (Spring ’05) The electric field ~ E generated by the two point charges, 3nC and q 1 (unknown), has the direction shown. (a) Find the magnitude of ~ E . (b) Find the value of q 1 . 2m 3nC 4m E 45 o y q 1 x Solution: (a) E y = k 3nC (2m) 2 = 6 . 75N / C , E x = E y , E = q E 2 x + E 2 y = 9 . 55N / C . (b) E x = k ( - q 1 ) (4m) 2 , q 1 = - (6 . 75N / C)(16m 2 ) k = - 12nC . tsl331 – p.1/4

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Intermediate Exam I: Problem #2 (Spring ’05) Consider a point charge Q = 5 nC fixed at position x = 0 . (a) Find the electric potential V 1 at position x 1 = 3 m and the electric potiential V 2 at position x 2 = 6 m. (b) If a charged particle ( q = 4 nC, m = 1 . 5 ng) is released from rest at x 1 , what are its kinetic energy K 2 and its velocity v 2 when it reaches position x 2 ? x = 0 x = 3m 1 x = 6m 2 Q = 5nC Solution: (a) V 1 = k Q x 1 = 15V , V 2 = k Q x 2 = 7 . 5V . (b) Δ U = q ( V 2 - V 1 ) = (4nC)( - 7 . 5V) = - 30nJ Δ K = - Δ U = 30nJ . Δ K = K 2 = 1 2 mv 2 2 v 2 = r 2 K 2 m = 200m / s . tsl332 – p.2/4
Intermediate Exam I: Problem #3 (Spring ’05) Consider two plane surfaces with area vectors ~ A 1 (pointing in positive x -direction) and ~ A 2

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