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Potential Energy of a System of Multiple Point Charges

Two identical...

Question

Two identical charges, $5 μ C$ , each are fixed at a distance $8 c m$ and a charged particle of mass $9 \times 10^{- 6} k g$ and charge $- 10 μ C$ is placed at a distance $5 c m$ from each of them and is released. Find the speed of the particle when it is nearest to the two charges.

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Solution

As there is no external force on the system, so the net change is Mechanical energy is 0.
$△ U_{s y s t e m} = △ K_{c h a r g e}$
From the diagram,
$U_{i} = \frac{K X (5 X 10^{- 6}) (- 10 X 10^{- 6})}{5 X 10^{- 2}} X 2$ $= - 20 K X 10^{- 10} J$

$U_{f} = \frac{K X (5 X 10^{- 6}) (- 10 X 10^{- 6})}{4 X 10^{- 2}} X 2$ $= - 25 K X 10^{- 10} J$
$△ U_{s y s} = U_{i} - U_{f} = 5 K X 10^{- 10} = 4.5 J$
Now,
$△ U = △ K = 1 / 2 m v^{2}$
$⟹ 4.5 = 0.5 X 9 X 10^{- 6} v^{2}$
$v = 1000 m / s$

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