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Two infinitely long line charges having ...

Two infinitely long line charges having charge density `lamda` each are parallel to each other and separated by distance d. A charge particle of mass m and charge q is placed at mid point between them. This charge displaced slightly along a line AB which is perpendicular to the line charges and in the plane of the charges. prove that the motion of the particle will be SHM for small displacement and `lamda q gt 0` Neglect gravity. Find the time period.

Text Solution

Verified by Experts

The correct Answer is:
`2 pi sqrt((md^(2) pi in_(0))/(4 lamdaq))`
`F=-2qk lamda((1)/((d)/(2)-x)-(1)/((d)/(2)+x))`
`rArr F = -((q lamda)/(pi epsilon_(0))(1)/((d^(2))/(4)))x :. T = 2 pi sqrt((md^(2) pi in_(0))/(4 lamda q))`
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