Figure shows a schematic view of an electrostatic analyzer. It can sort out charged particles by speed and charge to mass ratio. Spacecraft use such analyzers to characterize charged particles in interplanetary space. Two curved metal plates establish an electric field given by `E=E_(0)(b/r)` where `E_(0)` and b are positive constants with unit of electric field and length. The field points toward the centre of curvature and r is distance from centre. There is no influence of gravity. Proton (change `+e` mass 'm') enters along y-axis and exits along x-axis while moving along a circular path.

Speed with which protion is to be projected is 'v' and centripetal acceleration of electron is `'a_(c)'` is given by respectively. Mark the correct statement

Options

A. `v=sqrt((eE_(0)b)/m),a_(c)=(2e)/mE_(0)(b/r)`
B. `v=sqrt((2eE_(0)b)/m),a_(c)=e/(2m)E_(0)(b/r)`
C. `v=sqrt((eE_(0)b)/(2m)),a_(c)=(2e)/m E_(0)(b/r)`
D. `v=sqrt((eE_(0)b)/m),a_(c)=e/mE_(0)(b/r)`

Answer

D

Explanation

`eE=(mv^(2))/rRightarrowv=sqrt((eE_(0)b)/m)`
`a_(c)=(eE)/m=e/mE_(0)(b/r)`