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) .

A thin fixed ring of radius 'R' and positive charge 'Q' is placed in a vertical plane. A particle of mass 'm' and negative charge 'q' is placed at the centre of ring. If the particle is given a small horizontal displacement, show that it executes SHM. Also find the time period of small oscillations of this particle, about the centre of ring. (Ignore gravity)

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.

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 so that distance of this charge from each charge located at end is L. Assuming that the middle charge moves along the line joining the fixed charges. The frequency of oscillation when it is displaced slightly is

Two small particles charged with equal positive charges Q each, are fixed apart at a distance 2a. Another small particle having a charge q lies midway between the fixed charges. Show that (i) For small displacement (relative to a) along line joining the fixed charges, the middle charge executes SHM'if it is +ve and (ii) For small lateral displacement, it executes SHM ifit is-ve. Compare the frequencies of oscillation in the two cases

A particle of mass m and +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, show that the frequency of oscillation when it is displaced slightly is (q)/(2pi)sqrt((1)/(piepsilon_(0)ml^(3))

A charged particle q of mass m is in wquilibrium at a height h from a horizontal infinite line charge wit uniform linear charge density lambda . The charge lies in the vertical plane containing the line charge. If the particle is displaced slightly (vertically) prove that the motion of the charged particle will be simple harmonic. Also find its time period.

A charged particle q of mass m is in wquilibrium at a height h from a horizontal infinite line charge wit uniform linear charge density lambda . The charge lies in the vertical plane containing the line charge. If the particle is displaced slightly (vertically) prove that the motion of the charged particle will be simple harmonic. Also find its time period.