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Question

A uniform charged ring of radius R and charge Q is placed in horizontal plane. If a point charge q of mass m is placed on the axis of ring in equilibrium position, then which of the following option(s) is/are correct: [k=14πϵ0] 
  1. If we provide small displacement to the point charge in the vertical direction, it will execute S.H.M. .
  2. If we provide small displacement to the point charge in the vertical direction, it will execute oscillatory motion.
  3. If we provide small displacement to the point charge in the horizontal direction, it will execute S.H.M.
  4. The amplitude above the equilibrium position and below it, may be different.


Solution

The correct options are
B If we provide small displacement to the point charge in the vertical direction, it will execute oscillatory motion.
D The amplitude above the equilibrium position and below it, may be different.
At equilibrium position.
kQq(R2+x2)32x=mg
kQqmg=(R2+x2)32x
If we displace it by small distance 'y', then
F=kQq(x+y)[R2+(x2+y2)]32
As Fnet is not in the form of F y. So it will not do S.H.M.
Since Fnet is opposite to the displacement, motion
 

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