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Two Particles, Carrying Charges −Q and +Q and And of Mass M Each, Are Fixed at the Ends of a Light Rod of Length a to Form a Dipole.

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प्रश्न

Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.  

संख्यात्मक
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उत्तर

Consider the rod to be a simple pendulum
Time period of a simple pendulum, 

\[T = 2\pi\sqrt{\frac{l}{a'}}\]

(where l = length and a' = acceleration)

Now

\[a' = \frac{F}{m} = \frac{Eq}{m}\]
and length l = a
∴ The time period, 
\[T = 2\pi\sqrt{\frac{ma}{qE}}\]
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अध्याय 29: Electric Field and Potential - Exercises [पृष्ठ १२४]

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एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 29 Electric Field and Potential
Exercises | Q 74 | पृष्ठ १२४

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