Figure shows a large conducting ceiling having uniform charge particle of charge density `sigma` below which a charge particle of charge `q_0` and mass m is hung from point O, through a small string of length l. Calculate the minimum horizontal velocity v required for the string to become horizontal.
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Answer

`v = sqrt((2 l sigma q_0)/(m epsilon_0))`

Explanation

`W_("net") = Delta K E` or `-mgl - q_0 E l = 0 -(1)/(2) m v^2` or `v = sqrt((2 m g l + 2 q_0 E l)/(m))`
when `E = (sigma)/(epsilon_0)`.