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Question

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

Moderate

Solution

Let an electron be projected towards the plate from r distance as shown in fig.

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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Potential energy

Remember concepts with our Masterclasses.

A negatively charged plate has charge density of . The initial distance of an electron which is moving toward plate, cannot strike the plate, if it is having energy of 200 eV

Let an electron be projected towards the plate from r distance as shown in fig.It will not strike the plate if and only if KE e(E.r) (where E = Electric field due to charge plate )⇒ .Hence minimum value of r is given by

Ready to Test Your Skills?

free study material

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