question_answer

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 \[200\,eV\]                                             [RPET 1997]

A)                    \[1.77\,mm\]

B)                                      \[3.51\,mm\]

C)                    \[1.77\,cm\]

D)                                      \[3.51\,cm\]

Correct Answer: A

Solution :

           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 £ e(E×r)  (where E = Electric field due to charge plate \[=\frac{\sigma }{2{{\varepsilon }_{0}}}\]) Þ \[r\ge \frac{KE}{eE}\]. Hence minimum value of r is given by          \[r=\frac{KE}{eE}=\frac{200\,eV}{e\times \frac{\sigma }{2{{\varepsilon }_{0}}}}\]\[=\frac{400\times 8.86\times {{10}^{-12}}}{2\times {{10}^{-6}}}=1.77mm\]