Question

Two charges lie along the x-axis. One positive charge, q1 = 15 μC, is at x= 3.0m, and another positive charge, q2 = 6.0 μC, is at the origin. At what point on the x-axis is the

resultant electric field zero?

Answer 1

$$E_1=E_2,$$ $$\dfrac{kq_1}{x^2}=\dfrac{kq_2}{(3-x)^2},$$ $$q_1(3-x)^2=q_2x^2,$$ $$\dfrac{3-x}{x}=\sqrt{\dfrac{q_2}{q_1}},$$ $$x=\dfrac{3}{1+\sqrt{\dfrac{q_2}{q_1}}},$$ $$x=\dfrac{3\ m}{1+\sqrt{\dfrac{6.0\cdot10^{-6}\ C}{15.0\cdot10^{-6}\ C}}}=1.84\ m.$$