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प्रश्न
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. Assuming x<<d, show that this force is proportional to x.
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उत्तर
When x < < d:
\[F' = \frac{1}{2 \pi\epsilon_0}\frac{qQx}{\left( \frac{d}{2} \right)^3} \left( \because x^2 < < \left( \frac{d}{2} \right)^2 \right)\]
\[ \Rightarrow F' = \frac{4}{\pi\epsilon_0}\frac{qQx}{d^3}\]
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where the distance r is measured in cm (= 10–2 m), F in dynes (= 10–5 N) and the charges in electrostatic units (es units), where 1 es unit of charge = `1/([3]) xx 10^-9 C`
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or, `1/(4pi ∈_0) = (2.99792458)^2 xx 10^9 (Nm^2)/C^2` (exactly).
