A negatively charged plate has charge density of
$\large 2 \times {10^{ - 6}}C/{m^2}$
. The initial distance of an electron which is moving toward plate, cannot strike the plate, if it is having energy of 200 eV

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1.77 cm

1.77 mm

3.51 cm

3.51 mm

answer is A.

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Detailed Solution

Let an electron be projected towards the plate from r distance as shown in fig.
Question Image
It will not strike the plate if and only if KE $\large \leq$ e(E.r) (where E = Electric field due to charge plate $\large = \frac{\sigma }{{2{\varepsilon _0}}}$ )
⇒ $\large r \geqslant \frac{{KE}}{{eE}}$ .Hence minimum value of r is given by
$\large r = \frac{{KE}}{{eE}} = \frac{{200\,eV}}{{e \times \frac{\sigma }{{2{\varepsilon _0}}}}}$ $\large = \frac{{400 \times 8.86 \times {{10}^{ - 12}}}}{{2 \times {{10}^{ - 6}}}} = 1.77mm$