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An electron is projected from a distance...

An electron is projected from a distance `d` and with initial velocity `u` parallel to a uniformly charged flat conducting palte as shown. It strikes the plate after travelling a distance `l` along the direction of projection. The surface charge density of the conducting plate is equal to

A

`(2depsilon_(0)"mu"^(2))/(el^(2))`

B

`(2depsilon_(0)"mu")/(el)`

C

`(depsilon_(0)"mu"^(2))/(el)`

D

`(depsilon_(0)"mu")/(el)`

Text Solution

Verified by Experts

The correct Answer is:
A
For the motion of the electron along `Y` axis
`d=(1)/(2)(eE)/(m)*t^(2)`……….`(1)`
where `E` is the electric field due to the charged plate given by
`E=sigma//epsilon_(0)`………`(2)`
where `sigma` is the surface density of charge of the plate.
The time taken by the electron is
`t=(l)/(u)` ........`(3)`
From Eqs. `(1)`, `(2)` and `(3)`, we obtain
`d=(1)/(2)(esigma)/(epsilon_(0)m)((l)/(u))^(2)rArrsigma=(2depsilon_(0)"mu"^(2))/(el^(2))`
`:. (A)`
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