A particle of charge `-q` and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density `+lamda`. Then, time period will be
where , `k=1/4piepsilon_0)`

Options

A. `T=2pi rsqrt((m)/(2k lambdaq))`
B. `T^(2)=(4pi^(2)m)/(2k lambda q)r^(3)`
C. `T=(1)/(2 pi r) sqrt((2k lambdaq)/(m))`
D. `T=(1)/(2pi r) sqrt((m)/(2k lambdaq))`

Answer

A

Explanation

We have centripetal force equation
`q((2k gamma)/(r))=(mv^(2))/(r)`
so `v=sqrt((2kq gamma)/(m))` Now `T=(2pi r)/(v)=2pirsqrt((m)/(2 k gamma q))`
where, `k=(1)/(4pi epsilon_(0))`