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An $100 \mathrm{eV}$ electron is fired directly towards a large metal plate having surface charge density $-2 \times 10^{-6} \mathrm{Cm}^{-2}$. The distance from where the electron be projected, so that it just fails to strike the plate is
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The correct answer is:
$0.44 \mathrm{~mm}$
Given that, initial kinetic energy of electrons,
$K_i=100 \mathrm{eV}$
Initial potential energy, $U_i=0$
Let $K_f$ and $U_f$ be final kinetic and potential energies,
$\therefore \quad K_f=0$
By using law of conservation of energy,
$K_i+U_i=K_f+U_f$
$U_f=K_i$
$\Rightarrow \quad K_i=U_f=\frac{e d \sigma}{\varepsilon_0}$
Now, substituting the values, we get
$100 \times 1.6 \times 10^{-19}=\frac{1.6 \times 10^{-19} \times d \times 2 \times 10^{-6}}{8.85 \times 10^{-12}}$
$\Rightarrow \quad d=0.44 \times 10^{-3} \mathrm{~m}$
$=0.44 \mathrm{~mm}$
$K_i=100 \mathrm{eV}$
Initial potential energy, $U_i=0$
Let $K_f$ and $U_f$ be final kinetic and potential energies,
$\therefore \quad K_f=0$
By using law of conservation of energy,
$K_i+U_i=K_f+U_f$
$U_f=K_i$
$\Rightarrow \quad K_i=U_f=\frac{e d \sigma}{\varepsilon_0}$
Now, substituting the values, we get
$100 \times 1.6 \times 10^{-19}=\frac{1.6 \times 10^{-19} \times d \times 2 \times 10^{-6}}{8.85 \times 10^{-12}}$
$\Rightarrow \quad d=0.44 \times 10^{-3} \mathrm{~m}$
$=0.44 \mathrm{~mm}$
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