Question

A 100 eV electron is fired directly towards a large metal plate having surface charge density –2 × 10–6 Cm–2. The distance from where the electrons be projected so that it just fails to strike the plate is

Answer 1

(Correction: The numerical is supposed to be $-2$ × $-10^-^6cm^-^2$)

We know that,

The total energy of the system will always remain at a constant value.

So,

$K.E._1 + P.E._1 = K.E._2 + P.E._2$      

Now,

$P.E._1 = 0$          $K.E._2 = 0$

Thus, $K.E._1=P.E._2$

Now, according to the question,

$K.E._1= 100 eV$    ;     $P.E._2 =$ (edσ) ÷ (ϵ₀)

∴ The Distance (d) of the electron projection from the metal plate = ($K.E._1$ϵ₀) ÷ σ

⇒ d = (100 × 8.85 × $10^-^1^2$) ÷ (2 × $10^-^6$) = 0.44 m

Ans) The Distance of the electron projection from the metal plate is 0.44 m