Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Two Particles a and B, Each Carrying a Charge Q, Are Held Fixed with a Separation Dbetween Them. Find the Time Period of the Oscillations If These Conditions Are Satisfied. - Physics

Short Note

Two particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB.   Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement? Find the time period of the oscillations if these conditions are satisfied.

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For the particle to execute simple harmonic motion:
F' = mw2x

\[\Rightarrow \frac{4}{\pi \epsilon_0}\frac{qQx}{d^3} = m \left( \frac{2\pi}{T} \right)^2 x\] 

\[ \Rightarrow  T^2  = \frac{m \pi^3 \epsilon_0 d^3}{Qq}\] 

\[\Rightarrow T= \left[ \frac{m \pi^3 \epsilon_0 d^3}{Qq} \right]^{1/2} \] 

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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 7 Electric Field and Potential
Q 32.3 | Page 122
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