# Don't hammer the charge particle , he is innocent !

Consider two fixed identical uniformly charged solid cylinder's having volume charge density $$\rho$$ and radius $$R$$ length $$L$$ each and separated by distance $$d$$. If a point charge is kept at a mid point of these cylinder on their axis, so that system is in equilibrium. Then find time period of small vertical oscillation of charged particle. If it expressed as:

$\displaystyle{T=2\pi \sqrt { \cfrac { a\sqrt { b } +c\sqrt { d } }{ e } \left( \cfrac { m\epsilon }{ q\rho } \right) } }$

Find least value of $$a+b+c+d+e$$

Details and assumptions:

• $$R=1 \text{ m}, L=1 \text{ m}, d=2 \text{ m}$$

• $$\epsilon$$ is permittivity of free space and neglect gravity.

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