Question

Two particles having charges 𝑞₁ = 1.00 × 10⁻¹⁹𝐶 and 𝑞₂ = 2.00 × 10⁻⁹𝐶 are separated by a distance 2.00m. At what point is the total electric field due to the two charges equal to zero? 

Answer 1

$\vec{E_1}+\vec{E_2}=0$ initial conditions

$E=\frac{kq}{r^2}$ electric field

$$\frac{q_1}{r_1^2}=\frac{q_2}{(l-r_1)^2}$$ $$r_1=\frac{l}{\sqrt{\frac{q_2}{q_1}}+1}$$

Calculating

$r_1=\frac{2}{\sqrt{\frac{2\cdot10^{-19}}{1\cdot10^{-9}}}+1}\approx1.99997...$

Answer electric field equal to zero on distances 1.99 metres from q1