There is a fixed sphere of radius R having positive charge Q uniformly spread in its volume. A small particle having mass m and negative charge `(– q)` moves with speed V when it is far away from the sphere. The impact parameter (i.e., distance between the centre of the sphere and line of initial velocity of the particle) is b. As the particle passes by the sphere, its path gets deflected due to electrostatics interaction with the sphere.
(a) Assuming that the charge on the particle does not cause any effect on distribution of charge on the sphere, calculate the minimum impact parameter b0 that allows the particle to miss the sphere. Write the value of `b_(0)` in term of R for the case
`1/2mV^(2)=100.((kQq)/(R))`
(b) Now assume that the positively charged sphere moves with speed V through a space which is filled with small particles of mass m and charge – q. The small particles are at rest and their number density is n [i.e., number of particles per unit volume of space is n].
The particles hit the sphere and stick to it. Calculate the rate at which the sphere starts losing its positive charge `(dQ)/(dt).` Express your answer in terms of `b_(0)`

Answer

`(a) b_(0) = R sqrt(1+(2KQq)/(mRV^(2)) ) " "b_(0)cong 1.02 R
`(b) qnpib_(0)^(2)VB`