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A positively charged particle P enters t...

A positively charged particle P enters the region between two parallel plates with a velocity u, in a direction parallel to the plates. There is a uniform electric field in this region. P emerges from this region with a velocity v. Taking C as a constant, v will depend on u as

A

`v = Cu`

B

`v = (sqrt(u^2+Cu))`

C

`v = (sqrt(u^2+C/u))`

D

`v = (sqrt(u^2 + C/u^2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`l` is the length of the each tube `u_(x)=u` constant. Time of travel between the plates is `t=l//u` let `a` be constant acceleration in y-direction so `v_(y)=at` when the particle emerges from the plates so
`v^(2)=u_(x)^(2)+v_(y)^(2)=u^(2)+a^(2)t^(2)`
`=u^(2)+a^(2)(l^(2))/(u^(2))=u^(2)+(C)/(u^(2))` (where `a^(2)l^(2)=C`)
So, `v=sqrt(u^(2)+(C)/(u^(2)))`
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