A particle of mass `m`and charge `q`, moving with velocity `v` enters Region `II` normal to the boundary as shown in the figure. Region `II` has a uniform magnetic field `B` perpendicular to the plane of the paper . The length of the region `II` is `l`. Choose the correct choice(s).

Options

A. The particle enters Region `III` only if its velocity ` v lt (qlB)/(m)`
B. The particle enters Region `III` only if its velocity ` v gt (qlB)/(m)`
C. Path length of the particle in Region `II` is maximum when velocity `v = (qlB)/(m)`
D. Time spent in Region `II` is same for any velocity `v` as long as the particle returns to Region `I`

Answer

A, C, D

Explanation

As the particle enters the magnetic field , a force acts on it due to the magnetic field which moves the particle in a circular path of radius
` r = ( mv)/(q^(B))`
* for the particle to enter region III, ` rgt l ( path shown by dotted line )
rArr (mv)/(q^(B)) gt l rArr v gt ( qlB)/(m)`
* For maximum path length in region II , ` r = l `
:. l = (mv)/(q^(B)) rArr v = (qlB)/(m) `
* The time taken by the particle to move in region ` II` before coming back in region `I` is given by
` t = ( pi m)/(q^(B))` which is independent of `v`.