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253-wrk-23

# 253-wrk-23 - HPHY 253 Workout 23 Electric Fields Dr A E Bak...

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HPHY 253 Workout 23 Electric Fields Dr. A. E. Bak Name 1. A ° 4 : 50 - ° C particle lies at the location (in m ) of (1 : 00 ; 4 : 00) in the xy plane. Find the electric °eld that it produces at ( ° 1 : 00 ; 7 : 00) . The source charge here is q = ° 4 : 50 ° C = ° 4 : 50 ± 10 ° 6 C : We have r = length vector from (1 : 00 ; 4 : 00) to ( ° 1 : 00 ; 7 : 00) = ( ° 1 : 00 ° 1 : 00) e x + (7 : 00 ° 4 : 00) e y = ( ° 2 : 00 e x + 3 : 00 e y ) m ; having magnitude r = q ( ° 2 : 00) 2 + (3 : 00) 2 ² 3 : 606 m : Therefore, we obtain E = k e q r r 3 = ° 8 : 987551787 ± 10 9 ± ° ° 4 : 50 ± 10 ° 6 ± ( ° 2 : 00 e x + 3 : 00 e y ) (3 : 606) 3 = (1730 e x ° 2590 e y ) N= C as the electric °eld at ( ° 1 : 00 ; 7 : 00) due to the ° 4 : 50 - ° C point charge. 2. In the xy plane, a +6 : 00 - ° C particle lies at the location (in m ) of (0 : 300 ; 0) and a ° 3 : 00 - ° C particle lies at (0 ; 0 : 100) . Find the electric °eld that these charges together produce at the origin. ³ The electric °eld due to source charge q 1 : Consider the point charge q 1 = +6 : 00 ° C = +6 : 00 ± 10 ° 6 C : We have r 1 = length vector from (0 : 300 ; 0) to (0 ; 0) = (0 ° 0 : 300) e x + (0 ° 0) e y = ° 0 : 300 e x m ; having magnitude r 1 = 0 : 300 j = 0 : 300 m : Therefore, we obtain E 1 = k e q 1 r 1 r 3 1 = ° 8 : 987551787 ± 10 9 ± ° +6 : 00 ± 10 ° 6 ± ( ° 0 : 300 e x ) (0 : 300) 3 = ° 5 : 99 e x ± 10 5 N= C as the electric °eld at (0 ; 0) due to the +6 : 00 ° C point charge. ³ The electric °eld due to source charge q 2 : Consider the point charge q 2 = ° 3 : 00 ° C = ° 3 : 00 ± 10 ° 6 C : We have r 2 = length vector from (0 ; 0 : 100) to (0 ; 0) = (0 ° 0) e x + (0 ° 0 : 100) e y = ° 0 : 100 e y m ; having magnitude r 2 = 0 : 100 j = 0 : 100 m : Therefore, we obtain E 2 = k e q 2 r 2 r 3 2 = ° 8 : 987551787 ± 10 9 ± ° ° 3 : 00 ± 10 ° 6 ± ( ° 0 : 100 e y ) (0 : 100) 3 = 2 : 70 e y ± 10 6 N= C as the electric °eld at (0 ; 0) due to the ° 3 : 00 ° C point charge.

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253-wrk-23 - HPHY 253 Workout 23 Electric Fields Dr A E Bak...

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