Q Two fixed charges 4Q and 2Q are separated by a distance x Where should third point charge q to - Physics -

Question

Q Two fixed charges 4Q and 2Q are separated by a distance x
Where should third point charge q to b placed for it to be in
equilibrium ???

Hansraj Rai · Accepted Answer

Let the charge q is placed at at a distance x' from the charge 4Q.

SO, According to the problem force on q by both the charges are same.

Therefore,

$\frac{1}{4 π ϵ_{0}} \times \frac{(4 Q) q}{{x'}^{2}} = \frac{1}{4 π ϵ_{0}} \times \frac{(2 Q) q}{{(x - x')}^{2}}$

On solving we get,

$x' = \frac{\sqrt{2} x}{1 + \sqrt{2}}$

Q Two fixed charges 4Q and 2Q are separated by a distance x.Where should third point charge q to b placed for it to be in equilibrium ???