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Unformatted text preview: EE1 Spring 2008 Midterm Exam Solutions Problem 1 (25 pts) Two point charges Q 1 and Q 2 are located in free space at r 1 = ( x 1 , y 1 , z 1 ) and r 2 = ( x 2 , y 2 , z 2 ). Neither charge is at the origin. (a) What is the amplitude of the force that Q 1 exerts on Q 2 ? The amplitude of the force between two point charges is given by Coloumb’s Law.  F  = Q 1 Q 2 4 π  R F  2 where  R F  = q ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 + ( z 1 z 2 ) 2 (b) Calculate the total electric field amplitude at the origin. To calculate the total electric field amplitude we can add the con tribution of the electric field from each point charge. Charge Q 1 : E 1 = ˆ R 1 Q 1 4 π  R 1  where ˆ R 1 = x 1 ˆ x y 1 ˆ y z 1 ˆ z q x 2 1 + y 2 1 + z 2 1  R 1  = q x 2 1 + y 2 1 + z 2 1 Charge Q 2 : E 2 = ˆ R 2 Q 2 4 π  R 2  where ˆ R 2 = x 2 ˆ x y 2 ˆ y z 2 ˆ z q x 2 2 + y 2 2 + z 2 2 1  R 2  = q x 2 2 + y 2 2 + z 2 2 E tot = E 1 + E 2 = E x ˆ x + E y ˆ y + E z ˆ z where E x = 1 4...
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This note was uploaded on 06/18/2008 for the course EE 1 taught by Professor Joshi during the Spring '08 term at UCLA.
 Spring '08
 Joshi

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