A +8.0 nC charge is located at (x, y) = (0cm,11cm) and a -3.0 nC charge is locat

Question

A +8.0 nC charge is located at (x, y) = (0cm,11cm)   and a -3.0 nC charge is located 3.0 (x, y) =(3cm, 0cm) . Where would a -9.0 nC charge need to belocated in order that the electric field at the origin bezero? (x,y)= A +8.0 nC charge is located at (x, y) = (0cm,11cm)   and a -3.0 nC charge is located 3.0 (x, y) =(3cm, 0cm) . Where would a -9.0 nC charge need to belocated in order that the electric field at the origin bezero? (x,y)= Where would a -9.0 nC charge need to belocated in order that the electric field at the origin bezero? (x,y)=

Explanation / Answer

let the third charge(q3) be located at (x,y) so that theelectric field at the origin be zero
electric field due to charge q1 is E1 = k * (q1/r^2) k = (1/4o) = 9 * 10^9 Nm^2/C^2,q1 =+8.0 nC = +8.0 * 10^-9 C and r^2 = [(0 - 0)^2 + (0 - 11)^2]^(1/2) =11 electric field due to charge q2 is E2 = k * (q2/r1^2) q2 = -3.0 nC = -3.0 * 10^-9 C and r1^2 = [(3 - 0)^2 + (0 -0)^2] = 9 electric field due to charge q3 is E3 = k * (q3/r2^2) q3 = -9.0 nC = -9.0 * 10^-9 C and r2^2 = [(x - 0)^2 + (y -0)^2] = x^2 + y^2 the electric field at the origin is zero therefore E1 + E3 = 0 or  k * (q1/r^2) + k * (q3/r2^2) = 0 or (q1/r^2) = -(q3/r2^2) ----------(1) and E2 + E3 = 0 or k * (q2/r1^2) + k * (q3/r2^2) = 0 or (q2/r1^2) = -(q3/r2^2) ------------(2) solving equations (1) and (2) for x and y we get thecoordinates of q3.

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