Home
Class 12
PHYSICS
A unit negative charge with mass resides...

A unit negative charge with mass resides at the midpoint of the straight line of length 2a adjoining two fixed charges of magnitude `+Q` each. If it is given a very small displacement `x(x lt lt a)` in a direction perpendicular to the straight line, it will

A

come back to its original position and stay there

B

execute oscillations with frequency `(1)/(2pi)sqrt((Q)/(4piepsilon_(0)Ma^(3))`

C

fly to infinity

D

execute oscillations with frequency `(1)/(2pi)sqrt((Q)/(4piepsilon_(0)Ma^(2))`

Text Solution

Verified by Experts

`(**)` : Let `F_("net")` be the resultant force,
`F_("net")=2Fcostheta`
`=(2xxQ)/(4piepsilon_(0)(x^(2)+a^(2))).costheta`
`=(2xxQ)/(4piepsilon_(0)(x^(2)+a^(2))).(x)/(sqrt(x^(2)+a^(2)))`
`thereforeF_("net")=(2)/(4piepsilon_(0)).(Qx)/((x^(2)+a^(2))^(3//2))=(2)/(4piepsilon_(0)).(Qx)/(a^(3))(becausexltlta)`
Aunit negative charge execute oscillations with frequency,
`v=(1)/(2pi)sqrt((F_("net"))/(Mx))=(1)/(2pi)sqrt((2.Q)/(4piepsilon_(0)Ma^(3)))=(1)/(2pi)sqrt((Q)/(2piepsilon_(0)Ma^(3)))`
None of the given option is correct.
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

Consider the points lying on a straight line joining two fixed opposite charges. Between the charges there is

Two identical positive charges Q each are placed on the x axis at point (-a,0) and (a,0) A point charge of magnitude q is placed at the origin. For small displacement along x axis, the charge q executes simple harmonic motion if it is poitive and its time period is T_(1) . if the charge q is negative, it perform oscillations when displaced along y axis. in this case the time period of small oscillations is T_(2). find (T_(1))/(T_(2))

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

If p be the length of the perpendicular from the origin on the straight line x+2by=2p then what is the value of b?

What are the points on the axis of x whose perpendicular distance from the straight line x/p + y/q = 1 is p?