A +10nC charge is located at (x,y) = (0 cm, 10 cm) and a -5.0 nC charge is locat

Question

A +10nC charge is located at (x,y) = (0 cm, 10 cm) and a -5.0 nC charge is located (x,y) = (5.0 cm, 0 cm). Where would a -8 nC charge need to be located in order that the electric field at the origin be zero?

x,y= ___cm?

I tried using the formulas:
E1=kQ1/y^2
E1=kQ2/x^2
Enet=sqroot E1^2+E2^2(=r)
tan theta=e1/e2
tan-1theta+180=theta
then
x=rcostheta
y=rsintheta

I found it to be -8.2,4.1cm but these are the wrong answers. Could someone solve for me and explain their process please?

Explanation / Answer

Let - 15nC be located at (x cm, 0) => electric field at the origin is - 6k/(7)^2 - 15k/x^2 = 0 => x^2 = (15/6) * 7^2 => x = ± 11.07 cm. As both the charges are negative, they have to be on opposite sides of the origin for the field to be zero. => x = - 11.07 cm. => the second charge has to be located at (- 11.07 cm, 0) similar one hope helps

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