Question

A 72 nC charge is located at x = 3.00 m on the x-axis and an 8.0 nC charge is located at x = 7.0 m. At what point on the x-axis is the electric field zero?

Answer 1

Since the charges are the same sign, the point where Ex = 0 is clearly between them and closer to the 8.0 nC charge. The condition for

$E_x =0 \\ \frac{kq_1}{(x-x_1)^2} = \frac{kq_2}{(x_2-x)^2} \\ \sqrt{ \frac{q_1}{q_2} } = 3 \\ 3(x_2-x) = x-x_1 \\ 3(7 -x)=x-3 \\ 21 -3x=x -3 \\ 4x=24 \\ x=6 \;m$