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EE1 Midterm Solution

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

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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 0 | R F | 2 where | R F | = ( 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 0 | R 1 | where ˆ R 1 = - x 1 ˆ x - y 1 ˆ y - z 1 ˆ z x 2 1 + y 2 1 + z 2 1 | R 1 | = x 2 1 + y 2 1 + z 2 1 Charge Q 2 : E 2 = ˆ R 2 Q 2 4 π 0 | R 2 | where ˆ R 2 = - x 2 ˆ x - y 2 ˆ y - z 2 ˆ z x 2 2 + y 2 2 + z 2 2 1

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| R 2 | = 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 π 0 ( Q 1 | R 1 | 3 x 1 + Q 2 | R 2 | 3 x 2 ) E y = - 1 4 π 0 ( Q 1 | R 1 | 3 y 1 + Q 2 | R 2 | 3 y 2 ) E z = - 1 4 π 0 ( Q 1 | R 1 | 3 z 1 + Q 2 | R 2 | 3 z 2 )
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