There is an infinite line of uniform linear density of charge `+lamda`. A particle of charge `-q` & mass `m` is projected with initial velocity `v_(0)` at an angle `theta` with the line of charge from a distance `a` from it. The point charge moves in plane containing line charge and point of projection The speed of the particle of found to be minimum when it's distance from the line of charge is `ae^((npimepsi_(0)^(2)0//qlamda))`. The value of n is (ingnore gravity)

Answer

1

Explanation

`a_(y)=(qlamda)/(2piepsilon_(0)my)impliesv_(y)(dv_(y))/(dy)=(-qlamda)/(2piepsilon_(0)my)`
`impliesint_(v_(0)sintheta)^(0)v_(y)dv_(y)=(-qlamda)/(2piepsilon_(0)m_(o))int_(a)^(y)(dy)/(y)`
`impliesy_(max)``=``ae^(piepsilon_(0)v_(0)^(2)sin^(2)theta//qlamda)`