Question

Two point charges $+q$ and $-q$ are placed at a distance x apart. A third charge is placed in such a way so that all the three charges are in equilibrium. Then :

• A. unknown charge is $-4q/9$
• B. unknown charge is $-9q/4$
• C. it should be at $\left(x/3\right)$ from smaller charge between them
• D. none of the above

Answer 1

Answer: (D)

none of the above

For equilibrium the three charges must be collinear, otherwise the vector sum of forces on any of the charge due to other two charges would not be zero.

If third charge $Q$ is placed $a$ distance from $+q$ and $b$ from $-q$.

Then total force on it is $kQq/a^2-kQq/b^2$,

where $k=1/4\pi {ϵ}_o$

For system to be in equilibrium, this force should be zero.

$\Rightarrow a=b$, so third charge $Q$ should be placed at middle of two charges.

But then forces on $Q$ due to $+q$ and $-q$ would be in same direction and hence non-zero.

Thus this system cannot be in equilibrium no matter what the value of third charge $Q$ is.

So options A, B, C are incorrect.

option D should be chosen.