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Vectors and Its Types

A point charg...

Question

A point charge $q_{1} = 1.0 μ C$ is held fixed at origin. A second point charge $q_{2} = - 2.0 μ C$ and a mass $10^{- 4}$ kg is placed on the x-axis, 1.0 m from the origin. The second point charge is released from rest. Its speed when it is 0.5 m from the origin is $189 \times 10^{- x} m s^{- 1}$ . Find the value of x.

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Solution

initial energy of system = $\frac{1}{4 π ϵ} \frac{q_{1} q_{2}}{1}$
when $q_{1}$ reached x=0.5, energy of system = $\frac{1}{4 π ϵ} \frac{q_{1} q_{2}}{0.5} + \frac{1}{2} m v^{2}$
equating the two energy,
$\frac{1}{4 π ϵ} q_{1} q_{2} (\frac{1}{1} - \frac{1}{0.5}) = \frac{1}{2} m v^{2} \Rightarrow v = 18.9 m / s$

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