Three +2 ?C point charges are fixed in space in the following locations; the fir

Question

Three +2 ?C point charges are fixed in space in the following locations; the first at <1, 0, 0> cm, second at <2, 0, 0> cm, and a third at <-4, 0, 0> cm.

(a) Find the net electric field at the following locations; <0, 0, 0> cm, <-2, 0, 0> cm, <3, 0, 0> cm, <0, 0, 1> cm, <1, 1, 0> cm, <1, 1, 1> cm.

(b) For each location where you found the electric field, what is the force on a -3 ?C test charge.

Please help! And show work so I can understand how to solve

Explanation / Answer

at(0,0,0)

E=9*10^9*2*10^6(1/2^2+1/2^2-1/4^2)*10^4

=21.375 *10^7 N/C

F=E*Q=641.25N

at(-2,0,0)

E=9*10^9*2*10^6(1/3^2+1/4^2-1/2^2)*10^4

=-1.375*10^7 N/C

F=41.25N

at(3,0,0)

E=9*10^9*2*10^6(1/1^2+1/2^2-1/7^2)*10^4

=22.86*10^7 N/C

F=686 N

at(1,1,0)

E=9*10^9*2*10^6*10^4(1/1^2 j +1/1.414^2(sin(45(i+cos(45)j))+1/5.09^2(-sin(11.30)i+cos(11.30j))

=9*10^9*2*10^6*10^4(0.34547i+1.3907 j)

E=25.79*10^7 n/c

F=773.8 N

similarly do at(0,0,1)

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