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 The equilibrium of a charged particle , under the action of coulumbian forces alone can never be stable. Pls explain this statement.
Asked by ashutosharnold1998 | 28 Aug, 2019, 11:03: AM
answered-by-expert Expert Answer
Let us consider a charge +q is placed at mid point of line connecting two similar charges as shown in fig. 1.
Though the charge at centre is stable due to repulsive forces that are equal and acting at opposite direction,
if small displacement in vertical direction due to some thermal motion may disturb the stability.
As shown in figure, if charge is displaced vertically, reulsive forces will not cancel each other but give net reultant force
in vertical direction. Hence the charge escapes in vertical direction
 
It may appears that if a charge +q is placed at centre of cube which is holding similar charges +q at each vertex,
is stable and held at centre because the charge is subjected to equal and opposite repulsive forces along each body diagonal.
But rigorous analysis shows that potential minima occurs at centre of each side of face of the cube.
Hence the charge may escape through the centre of any face of cube if small displacement is given along that direction.
 
These examples explains the "Earnshaw's theorem " in electrostatics.
This theorem states that charged particles can not be confined in space by electrostatic forces alone
Answered by Thiyagarajan K | 28 Aug, 2019, 13:21: PM

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