Question

a) If two charges +7 x10^-9C and -6 x10^-9C are separated 0.04m suspended in air, at which point on the line that join both charges the magnitude of the electric field will be E = 0 N/C?

Answer 1

$$E_1+E_2=0,$$ $$E_1=-E_2,$$ $$\dfrac{kq_1}{x^2}=-\dfrac{kq_2}{(0.04-x)^2},$$ $$q_1(0.04-x)^2=-q_2x^2,$$ $$\dfrac{0.04-x}{x}=\sqrt{\dfrac{-q_2}{q_1}},$$ $$0.04=x\sqrt{\dfrac{-q_2}{q_1}}+x,$$ $$x=\dfrac{0.04\ m}{\sqrt{\dfrac{-q_2}{q_1}}+1}=\dfrac{0.04\ m}{\sqrt{\dfrac{-(-6\cdot10^{-9}\ C)}{7\cdot10^{-9}\ C}}+1}=0.021\ m.$$