EE1 Midterm Solution

EE1 Midterm Solution - EE1 Spring 2008 Midterm Exam...

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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 Coloumbs Law. | F | = Q 1 Q 2 4 | 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 = R 1 Q 1 4 | R 1 | where R 1 =- x 1 x- y 1 y- z 1 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 = R 2 Q 2 4 | R 2 | where R 2 =- x 2 x- y 2 y- z 2 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 x + E y y + E z z where E x =- 1 4...
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EE1 Midterm Solution - EE1 Spring 2008 Midterm Exam...

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