There is an infinite line of uniform linear density of charge `+lamda`. A particle of charge `-q` and mass 'm' is projected with initial velocity `v_(0)` at an angle `theta` with the line of charge at a distance 'a' from it. The speed of the particle is found to be minimum when its distance from the line of charge is `ae^((n pi mepsilon_(0)v_(0)^(2)sin^(2)theta//q lamda))`. Find the value of `n`. Neglect gravity

Answer

1

Explanation

`a_(y)=(qlamda)/(2piepsilon_(0)my)impliesV_(y)(dv_(y))/(dy)=(-qlamda)/(2piepsilon_(0)my)`
`implies int_(v_(0)sintheta)^(0)v_(y)dv_(y)=(-qlamda)/(2piepsilon_(0)m_(0))int_(a)^(y) (dy)/y`
`=y_(max)=ae^((pimepsilon_(0)v_(0)^(2)sin^(2)theta//q_(lamda))`