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An electric is fired directly towards ...

An electric is fired directly towards the center of a large metal plate that has excess negative charge with surface charge density `=2.0xx10^(-6) C//m^(2)`. If the initial kinetic energy of electron of electron is 100 eV and if it is to stop due to repulsion just as it reaches the plate, how far from the plate must it be fired ?

Text Solution

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here, `sigma = -2.0xx10^(-6) C//m^(2)`
Initial `K.E. = K_(0) = 100 eV`
`= 100xx1.6xx10^(-19) J = 1.6xx10^(-17) J`
Let the electron be fired at a distance s from the plate, Fig. From work energy theorem, work done `= F xx s` = loss in K.E.
`(-eE) s = K_(0)`

Now, electric field due to the plate (having some thickness), `E = sigma//in_(0)`
`:. -e (sigma)/(in_(0)) s = K_(0)`
`s = (in_(0) K_(0))/(-e sigma) = (8.85xx10^(-12)xx1.6xx10^(-17))/(-1.6xx10^(-1) (-2xx10^(6)))`
`= 4.43xx10^(-4)m`
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