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Two uniformly charged nonconducting spheres, each of radius R , are fixed in a gravity free space as shown in the figure. If an electron is released at rest from the point A , then its speed just before striking the other sphere is [ mass of electron = m e ]

Options

  1. A2 Q e 9 π ε 0 m e R
  2. B8 Q e 9 π ε 0 m e R
  3. C16 Q e 9 π ε 0 m e R
  4. D4 Q e 9 π ε 0 m e R

Correct answer

B. 8 Q e 9 π ε 0 m e R

Step-by-step solution

Using the conservation of mechanical energy, we get KQe R - KQe 9R = -KQe R + KQe 9 R + 1 2 mv 2 - 2 KQe 9 R + 2 KQe R = 1 2 mv 2 16 4 πε 0 eQ 9 R = 1 2 mv 2  ⇒  v = 8 Qe 9 πε 0 m e R

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