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A cavity of radius r is made inside a solid sphere. The volume charge density of the remaining sphere is ρ . An electron (charge e , mass m ) is released from rest inside the cavity from point P as shown in the figure. The centre of the sphere and centre of the cavity are separated by a distance a . The time after which the electron again touches the sphere is

Options

  1. A6 2 r ε 0 m e ρ a
  2. B2 r ε 0 m 6 ρ a
  3. C6 r ε 0 m e ρ a
  4. Dr ε 0 m e ρ a

Correct answer

A. 6 2 r ε 0 m e ρ a

Step-by-step solution

E = ρ a 3 ε 0 F = e E = e ρ a 3 ε 0 acceleration = ρ e a 3 m ε 0 & = 1 2 × ρ e a 3 m ε 0 × t 2 = 2 r ⇒ t = 6 2 r ε 0 m e ρ a The electron will move opposite to electronic field with constant acceleration along shown horizontal line of length = 2 r

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