A large flat metal surface has a uniform charge density `+sigma`. An electron of mass `m` and charge `u` and returns to it at point `B`. Disregard gravity . The maximum value of `AB` is

Options

A. `(vm epsilon_(0))/(sigma e)`
B. `(v^(2)m epsilon_(0))/(e sigma)`
C. `(v^(2)e)/(epsilon_(0)sigmam)`
D. `(v^(2)sigma e)/(epsilon_(0) m)`

Answer

B

Explanation

Field near metal surface `E=(sigma)/(epsilon_(0))`
Force on electron `=eE=(e sigma)/(epsilon_(0))`
Acceleration of electron `a=(e sigma)/(m epsilon_(0))`
It will act as projectile with max range
`(u^(2))/a=(u^(2))/(e sigma) xxm epsilon_(0)`