Question

Point charges +4q, − qand +4qare kept on the x −axis at points x = 0, x = aand x = 2arespectively, then (a)Only qis in stable equilibrium(b)None of the charges are in equilibrium(c)All the charges are in unstable equilibrium(d)All the charges are in stable equilibriumplzzz explain this

Answer 1

The correct answer is (d) i.e. all the charges are in stable equilibrium .

Explanation :

• Magnitude of point charge kept at x = 0 is +4q

• Magnitude of point charge kept at x = a is -q

• Magnitude of point charge kept at x = 2a is +4q
• Now the net force acting on the charge +4q will be given as :

    $F_{4q} = \frac{K.4q.4q }{(2a)^2}- \frac{K.q.4q}{a^2}$  ( due to charges +4q and -q , and due to opposite signs of charges the two two forces are in opposite directions )

So, $F_{4q} = \frac{K.q.4q }{(a)^2}- \frac{K.q.4q}{a^2}$

            = 0

• Similarly net force on other +4q charge and -q charge is also 0.
• So the net force on all the charges is zero .

Hence , all the charges are in stable equilibrium .