A POINT CHARGE q OF SMALL MASS m IS PROJECTEDWITH VELOCITY V FROM ONE END OF A PARALLEL PLATE CAPACITOR - Physics - Electrostatic Potential And Capacitance

Question

A POINT CHARGE q OF SMALL MASS m IS PROJECTEDWITH VELOCITY V FROM
ONE END OF A PARALLEL PLATE CAPACITOR WITH PLATE AREA L*L AND
SEPARATION d BETWEEN THEM FOR WHAT VALLUE OF V q WILL JUST MISS THE
UPPER PLATE
A 2√(mgd+qE/m)
B √((qE/md-g)l)
C √((qE/md+g)l)
d √(2(mgd-qE/m ))

Ved Prakash Lakhera · Accepted Answer

q charge being positive , the electric force acting on it is in the downward direction along with weight of the charge i
 e
 qE +mg =m a       or        a = qE +mgm-----1
If charge q is just able to reach a height of 'd' then according to  third equation of motion,0 =v2 sin2450 -2 a d          or             a = v2 sin2452 d        or    a = v24 d-----2
from eqn 1 and 2 , we get,v24 d  =  qE +mgm        or       v2 = 4 d qE +mgm         or    v = 2  d qE +mgm     
Therefore option A
 IS THE RIGHT CHOICE

A POINT CHARGE q OF SMALL MASS m IS PROJECTEDWITH VELOCITY V FROM ONE END OF A PARALLEL PLATE CAPACITOR WITH PLATE AREA L*L AND SEPARATION d BETWEEN THEM .FOR WHAT VALLUE OF V q WILL JUST MISS THE UPPER PLATEA. 2√(mgd+qE/m)B. √((qE/md-g)l)C. √((qE/md+g)l)d. √(2(mgd-qE/m ))

A POINT CHARGE q OF SMALL MASS m IS PROJECTEDWITH VELOCITY V FROM ONE END OF A PARALLEL PLATE CAPACITOR WITH PLATE AREA L*L AND SEPARATION d BETWEEN THEM .FOR WHAT VALLUE OF V q WILL JUST MISS THE UPPER PLATE
A. 2√(mgd+qE/m)
B. √((qE/md-g)l)
C. √((qE/md+g)l)
d. √(2(mgd-qE/m ))