The distance between two fixed positive charges 4e and e is λ . How should a third charge ‘q’ be arranged for it to be in equilibrium? Under what condition will equilibrium of the charge ‘q’ be stable (for displacement on the line joining 4e and e) or will it be unstable?
Text Solution
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from charge 4 e (If q is positive stable, If q is negative unstable)
Sol.
The charge 'q' cannot be placed in the region I and III for it to be in equilibrium [whether it is positive or negative]
Only region is II, where equilibrium can be attained.
Let charge q is placed at distance 'x' from 4e.
Equating the forces, we get.
or 4 = 
or 
= 2
∴ x = 2 λ – 2x or x = 
∴ Charge q has to be placed at distance 
from 4e
If q is +ve, then on displacing slightly from point P the charge will return back to P
∴ Stable equilibrium
If q is negative, then on displacing slightly from P, charge will be attracted towards the charge towards which it is displaced.
∴ Unstable equilibrium
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