Question

Two point charges +4q and +q are placed at a distance L apart. A third charge Q is so placed that all the three charges are in equilibrium. Then location and magnitude of third charge will be

• A. At a distance$\frac{L}{3}$ from +4q charge,$\frac{4q}{9}$
• B. At a distance $\frac{L}{3}$ from +4q charge, $- \frac{4q}{9}$
• C. At a distance $\frac{2L}{3}$from +4q charge,$- \frac{4q}{9}$
• D. At a distance $\frac{2L}{3}$from +q charge, $+ \frac{4q}{9}$

Answer 1

Answer: (C)

At a distance $\frac{2L}{3}$from +4q charge,$- \frac{4q}{9}$

Answer 2

Let third charge be placed at a distance $x_{1}$ from +4q charge as shown

Now $x_{1} = \frac{L}{1 + \sqrt{\frac{q}{4q}}} = \frac{2L}{3}$ $\Rightarrow$ $x_{2} = \frac{L}{3}$

For equilibrium of q, $Q = + 4q\left( \frac{L/3}{L} \right)^{2} = \frac{4q}{9} \Rightarrow Q = - \frac{4q}{9}$.