Home
Class 12
PHYSICS
A particle of mass m and charge q is loc...

A particle of mass m and charge q is located midway between two fixed charged particles each having a charge q and a distance 2l apart. Prove that the motion of the particle will be SHM if it is displaced slightly along the line connecting them and released. Also find its time period.

A

`sqrt((pi^(3)Mepsilon_(0)d)/(Qq))`

B

`sqrt((pi^(2)Mepsilon_(0)d^(3)/(Qq))`

C

`sqrt((pi^(3)Mepsilon_(0)d^(3))/(Qq))`

D

`sqrt((pi^(3)Mepsilon_(0))/(Qqd^(3))`

Text Solution

Verified by Experts

The correct Answer is:
c

Let a charge q is displaced by x from the mean position as shown in the figure (ii).
The restoring force acting on the charge q to bring it in its mean position is
`F=-[(1)/(4piepsilon_(0))(Q)/((d-x)^(2))-(1)/(4piepsilon_(0))(Qq)/((d+x)^(2))]`
`=-(Qq)/(4piepsilon_(0))[(1)/((d-x)^(2))-(1)/((d+x)^(2))]`
`=-(Qq)/(4piepsilon_(0))[((d+x)^(2)-(d-x)^(2))/((d^(2)-x^(2))^(2))]=(Qq)/(4piepsilon_(0))[(4dx)/((d^(2)-x^(2))^(2))]`
Since `xltltd`
`thereforeF=-(Qq)/(4piepsilon_(0))[(4dx)/(d^(4))]=-(Qqx)/(piepsilon_(0)d^(3))`
Acceleration , `a=(F)/(M)=-(Qqx)/(piepsilon_(0)d^(3)M)` ...(i)
As `aprop-x`
The charge will execute simple harmonic motion . The standard equation of SHM is
`a=-omega^(2)x` (ii)
Comparing (i) and (ii) , we get
`omega^(2)=(Qq)/(piepsilon_(0)d^(3)M)oromegasqrt((Qq)/(piepsilon_(0)d^(3)M))`
Time period , `T=(2pi)/(omega)=2pisqrt((piepsilon_(0)Md^(3))/(Qq))=2sqrt((pi^(3)epsilon_(0)Md^(3))/(Qd))`
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATICS

    MTG-WBJEE|Exercise (WB JEE Previous Years Questions ) CATEGORY 3 : One or More than One Opion correct Type|4 Videos

  • ELECTROSTATICS

    MTG-WBJEE|Exercise (WB JEE Previous Years Questions ) CATEGORY 1 : Single Option correct Type|23 Videos

  • ELECTROMAGNETIC WAVES

    MTG-WBJEE|Exercise WB JEE WORKOUT (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|10 Videos

  • GRAVITATION

    MTG-WBJEE|Exercise WB JEE Previous Years Questions (CATEGORY 1: Single Option Correct Type|7 Videos

Similar Questions

Explore conceptually related problems

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 infinitely long line charges having charge density lamda each are parallel to each other and separated by distance d. A charge particle of mass m and charge q is placed at mid point between them. This charge displaced slightly along a line AB which is perpendicular to the line charges and in the plane of the charges. prove that the motion of the particle will be SHM for small displacement and lamda q gt 0 Neglect gravity. Find the time period.

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released, the kinetic energy attained by the particle after moving a distance y will be

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 moves along a diameter of a uniformluy charged sphere of radinus R and carrying a total charge +Q . Find the frequency of S.H.M. of the particle if the amplitude does not exceed .

As shown in the adjoining figure two charge particles each having charge q and mass m and d distance apart from each other. If two particle in equilibrium under the gravitational and electric force, then determine the ratio q//m .

A particle of mass m carrying a charge -q_(1) starts moving around a fixed charge +q_(2) along a circulare path of radius r. Find the time period of revolution T of charge -q_(1) .