Question

Charge A(qA=1C) and charge B(qB=2C) are 2 m apart. Charge C(qC=2C) is located between them, and the force on charge C is zero. How far from charge A is charge C?

Answer 1

Given,

Charge A and charge B are 2 m apart.

Let Charge A and Charge C are x m apart

Since force at C is zero.

Thus the force on C due to A and due to B is same

So,

$\begin{gathered} F_{AC}=F_{BC} \\ \Rightarrow k\frac{1C\times2C}{x^2}=k\frac{2C\times2C}{(2-x)^2} \\ \Rightarrow2(2-x)^2=4x^2 \\ \Rightarrow x^2+4x-4=0 \\ \Rightarrow x=\frac{-4\pm\sqrt[]{4^2-4\times1(-4)}}{2\times1} \\ \Rightarrow x=-2\pm2\sqrt[]{2} \\ \Rightarrow x=0.82,-4.82 \end{gathered}$

Since distance cannot be negative.

Thus the distanec between A and C is 0.82 m