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A particle with charge e and mass m, mov...

A particle with charge e and mass m, moving along the X-axis with a uniform speed u enters a region where a uniform electric field E is acting along the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any effect of gravity) is

A

`(2m u^(2))/(eE)`

B

`(eE)/(2m u^(2))`

C

`(m u)/(2eE)`

D

`(m u^(2))/(2eE)`

Text Solution

Verified by Experts

The correct Answer is:
d
Suppose a particle of mass m , moving along x -axis experiences a force , F = qE=eF.
It covers distance along x - axis `x=ut+1//2a_(x)t^(2)`
`x=ut ort=(x)/(u)` … (i)
Particle enters a region where a uniform electric field E is acting along the y - axis,
`y=u_(y)t^(2)+(1)/(2)a_(y)t^(2)`
`y=0+(1)/(2)xx(eE)/(m)xx((x)/(u))^(2)=(eE.x^(2))/(m u^(2))`
For parabola ,`x^(2)=4ay`
`thereforex^(2)=(4axxeExxx^(2))/(2 m u^(2))or a=( m u^(2))/(2eE)`
Focal length of the parabolic path is `(m u^(2))/(2eE)`
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