A negatively charged plate has charge density of $2 \times {10^{ - 6}}\,C/{m^2}$. The initial distance of an electron which is moving toward plate, cannot strike the plate, if it is having energy of $200\,eV$
Diffcult
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(a) Let an electron is projected towards the plate from the $r$ distance as shown in fig.
It will not strike the plate if and only if $KE \leq e(E\cdot r)$ (where $E$ $=$ Electric field due to charge plate $ = \frac{\sigma }{{2{\varepsilon _0}}}$)
$==>$ $r \ge \frac{{KE}}{{eE}}$. Hence minimum value of $r$ is given by
$r = \frac{{KE}}{{eE}} = \frac{{200\,eV}}{{e \times \frac{\sigma }{{2{\varepsilon _0}}}}}$$ = \frac{{400 \times 8.86 \times {{10}^{ - 12}}}}{{2 \times {{10}^{ - 6}}}} = 1.77\,mm$
It will not strike the plate if and only if $KE \leq e(E\cdot r)$ (where $E$ $=$ Electric field due to charge plate $ = \frac{\sigma }{{2{\varepsilon _0}}}$)
$==>$ $r \ge \frac{{KE}}{{eE}}$. Hence minimum value of $r$ is given by
$r = \frac{{KE}}{{eE}} = \frac{{200\,eV}}{{e \times \frac{\sigma }{{2{\varepsilon _0}}}}}$$ = \frac{{400 \times 8.86 \times {{10}^{ - 12}}}}{{2 \times {{10}^{ - 6}}}} = 1.77\,mm$
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