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In the arrangement shown in fig. two pos...

In the arrangement shown in fig. two positive charges, +Q each,are fixed. Mark the correct statement(s) regarding a third charged particle -q palce at the midpoint P that can be displaced along or perpendicular to the line connecting the charges.

A

The particle will perform SHM of `xltlta`.

B

The particle will oscillate about P but oscillate about P but not harmonically for any x.

C

The particle will perform SHM for `yltlta`.

D

The particle will oscillate about P but not harmonically for y comparable to a.

Text Solution

Verified by Experts

The correct Answer is:
C, D
The particle will oscillate or perform SHM if equilibrium is a stable one. For negative chargem equilibrium is stable if the particles are displaced along CD and unstabe for displacement along AB.

For `yltlta`, in displaced position, net resultant force towards equilibrium position is
`F_("res")=2F sin theta=(2xxQ)/(4 pi epsilon_(0)(a^(2)+y^(2)))xx(y)/((a^(2)+y^(2))^(1//2))=(2Qy)/(4 pi epsilon_(0)a^(3))[agtgty]`
`F_("res") prop y`, so SHM for `ygtgta`.
For `y~=a`, there would be restoring force, but F is not proportional to y. So there is oscillatory motion but not SHM.
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