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Two point charges each of charge ‘q’ are moving towards the centre ‘O’ of an earthed spherical conducting shell of radius R with the constant velocities v and 2v as shown in the figure . The choose the correct options (s)

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Where $r_{1} = 2 R$ and $r_{2} = 4 R$ , the current flowing from the spherical conducting shell to the earth is $(\frac{3 q v}{8 R})$

Where $r_{1} = 2 R$ and $r_{2} = 4 R$ , the charge on the spherical conducting shell is $(\frac{- 3 q}{4})$

Where $r_{1} = 2 R$ and $r_{2} = 4 R$ , the charge on the spherical conducting shell is $- \frac{3 q}{2}$

Where $r_{1} = 2 R$ and $r_{2} = 4 R$ , the current flowing from the spherical conducting shell to the earth is $(\frac{3 q v}{4 R})$

answer is A, C.

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Detailed Solution

$\frac{KQ}{R} + \frac{Kq}{f_{1}} + \frac{Kq}{f_{2}} = 0 Q = - qR (\frac{1}{r_{1}} + \frac{1}{r_{2}})$

When $r_{1} = 2R$ and $r_{2} = 4 R$

$Q = - qR (\frac{1}{2R} + \frac{1}{4R}) Q = - \frac{3q}{4} N o w, I = \frac{dQ}{dt} = q R (\frac{1}{r_{1}^{2}} \frac{{dr}_{1}}{dt} + \frac{1}{r_{2}^{2}} \frac{{dr}_{2}}{dt}) I = - qR (\frac{v}{r_{1}^{2}} + \frac{2v}{r_{2}^{2}})$

When $r_{1} = 2R$ and $r_{2} = 4 R$

$I = - qRv (\frac{1}{{4R}^{2}} + \frac{2}{{16R}^{2}}) I = - (\frac{3qv}{8R}) | I | = \frac{3qv}{8R}$

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