A change q is slightly displaced along the line joining both fixed charges Q. Find time period of oscillations of charge q.

A charged particle of mass m having charge q remains in equilibrium at height d above a fixed charge Q . Now the charged particle is slightly displaced along the line joining the charges, show that it will executes S.H.M. and find the time period of oscillation.

Two points charges , each Q , are fixed at separation 2d . A charged particle having charge q and mass m is placed between them. (a) Now this charged particle is slightly displaced along the line joining the charges , slow that it will execute simple harmonic motion and find the time period of oscillation. (b) If charge q is negative and it is displaced slightly perpendicular to the line joining the charges , repeat the part (a) .

Two positively charged particles each having charge Q and are d distance apart. A third charge is introduced in midway on the line joining the two charges. Find the nature and magnitude of third charge so that the system is in equilibrium.

A particle of mass m and charge +q is located midway between two fixed charged particles each having a charge +q and at a distance 2L apart. Assuming that the middle charge moves along the line joining the fixed charges, calculate the frequency of oscillation when it is displaced slightly.

two similar point charge + q are kept on x- axis at (-a,0)& (a,0) and another charge -Q of mass m Is kept at origin .If -Q si slightly displaced along y- axis & released them its time period of oscillation is -

A charge Q is placed at the centre of the line joining two point charges +q and +q as shown in figure. The ratio of charges Q and q is

In a free space, a thin rod carrying uniformly distributed negative charge -q is placed symmetrically along the axis of a tin ring of radius R varrying uniformly dostributed charge Q. The mass of the rod is m and length is l=2R . The ring is fixed and the rod is free to move. The rod is displaced slightly along the axis of the ring and then released. Find the period T to the small amplitude oscillations of the rod.