A ball of mass of 1 kg and charge `50 mu C` is directly projected from infinity toward another fixed ball of charge `1//6 mu C` ( as shown in Fig. 24-5). The initial velocity of projection is 10 m/s. Find the distance and its velocity at the closest separation. Assume that the initial line of motion is at a distance of 1 m from the second fixed charge.

Explanation

To solve the problem, we need to analyze the motion of the charged ball as it approaches the fixed charged ball. We will use the principles of energy conservation and electrostatic force.

### Given Data:
- Mass of the moving ball, \( m = 1 \, \text{kg} \)
- Charge of the moving ball, \( q_1 = 50 \, \mu C = 50 \times 10^{-6} \, C \)
- Charge of the fixed ball, \( q_2 = \frac{1}{6} \, \mu C = \frac{1}{6} \times 10^{-6} \, C \)
- Initial velocity of the moving ball, \( v_0 = 10 \, \text{m/s} \)
- Initial distance from the fixed charge, \( r_0 = 1 \, m \)
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