Two particles each of mass m and charge q are separated by `r_(1)` and the system is left free to move at t = 0. At t = 1, both the particles are found to be separated by `r_(2)`. The speed of each particle is

Options

A. `(qm)/(4piepsilon_(0)r_(1)r_(2))`
B. `(q)/(r_(1)r_(2)sqrt((r_(2)^(2)-r_(1)^(2))//4piepsilon_(0)m))`
C. `(sqrt(2)q)/(r_(1)r_(2)sqrt((r_(2)^(2)-r_(1)^(2))//4piepsilon_(0)m))`
D. `qsqrt(((r_(2)-r_(1)))/(4piepsilon_(0)mr_(1)r_(2)))`

Explanation

Since the particles are of same mass thus each particle will have same speed.
Initial energy `E_(i)=(1)/(4piepsilon_(0))(q^(2))/(r_(1))+0`
Final energy, `E_(f)=(1)/(4piepsilon_(0))(q^(2))/(r_(2))+(1)/(2)mv^(2)+(1)/(2)mv^(2)=(1)/(4piepsilon_(0))(q^(2))/(r_(2))+mv^(2)`
As the field is conservative,
Hence applying COE,
`(1)/(4piepsilon_(0))(q^(2))/(r_(1))=(1)/(4piepsilon_(0))(q^(2))/(r_(2))+mv^(2)`
`therefore mv^(2)=(q^(2))/(4piepsilon_(0))((1)/(r_(1))-(1)/(r_(2)))`
`therefore v=qsqrt(((r_(2)-r_(1)))/(4piepsilon_(0)mr_(1)r_(2)))`