Two equally charged, identical metal spheres $A$ and $B$ repel each other with a force '$F$'. The spheres are kept fixed with a distance '$r$' between them. A third identical, but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is

Two positively charged spheres of masses $m_1$ and $m_2$ are suspended from a common point at the ceiling by identical insulating massless strings of length $l$. Charges on the two spheres are $q_1$ and $q_2$, respectively. At equilibrium, both strings make the same angle $\theta$ with the vertical. Then

Force of attraction between two point charges $Q$ and $-Q$ separated by $d\,$ metre is ${F_e}$. When these charges are placed on two identical spheres of radius $R = 0.3\,d$ whose centres are $d\,$ metre apart, the force of attraction between them is

Identify the wrong statement in the following. Coulomb's law correctly describes the electric force that

Why Coulombian force is called two body force ?

Total charge $-\,Q$ is uniformly spread along length of a ring of radius $R$. A small test charge $+q$ of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring.

$(a) $ Show that the particle executes a simple harmonic oscillation.

$(b)$ Obtain its time period.