Question

Q1 Q2 A charge of-3.5 x 10-9 C is at the origin and a charge of 6.9 × 10-9 C is on the x-axis at x = 3 m. At what location on the x- axis is the electric ficld zero?

Answer 1

Given Q_1 = -35 times 10^-9 c Q_2 = 69 times 10^-9 c E_1 bar = E_2 bar1/ 4 pi t_0 Q/r_1^2 = 1/4 pi t_0 P_2/r_2^2 but r_2 = r_1 + 3 m 1/4 pi t_0 Q_1/r_1^2 = 1/4 pi t_0 Q_2/(r_1 + 3m)^2 cancelling common terms Q_1/r_1^2 = P_2/(r_1 + 3m)^2 (r_1 + 3m)^2/r_1^2 = P_2/Q_1 Assuming only magnitudes for Q_1 and a (r_1 + 3m)/r_1 = squareroot Q_2/Q_1 (r_1 + 3m)/r_1 = squareroot 6.9/3.5 r_1 + 3m = 1.404 r_1 3m + 1.404 r_1 - r_1 3m = 0.404 r_1 r_1 = 7.4259 or 7.426 Thus at - 7.426 m on x axis the electric field is zero.