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Q.

 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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a

1.77 cm

b

1.77 mm

c

3.51 cm

d

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

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