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

Electricity and Magnetism Level 5

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.

Original !
Try more Deepanshu's mixing of concepts

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