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A particle of mass m and charge (-q) ent...

A particle of mass m and charge (-q) enters the region between the two charged plates initrally moving along X-axis with speed `V_(x)` as shown in figure. The length of plate is L and an uniform electric field E is maintained between the plates. S.T. vertical deflection of the particle at the edge of the plate is `(qEL^(2))/(2mV_(x)^(2))`.

Text Solution

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Force on particle towards upper plate `B,F_(y)^(-)=qE`
Vertical acceleration of particle `a_(y)=(qE)/(m)`
Initial vertical velocity `V_(y)=0`
Time taken by praticle between the plates `t=(L)/(V_(x))`
From equation of motion `s=ut+(1)/(2)at^(2)`
Vertical deflection `y=0+(1)/(2)a_(y)t^(2)`
`=0+(1)/(2)((qE)/(m))((L)/(V_(x)))^(2)`
`y=(qEL^(2))/(2mV_(x)^(2))`
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