# A 100 eV electron is fired directly towards a large metal plate having surface charge density…

Q: 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 electron be projected so that it just fails to strike the plate is

(a) 0.22 mm

(b) 0.44 mm

(c) 0.66 mm

(d) 0.88 mm

Ans:(b)

Sol: Here, K.E. = 100 eV = 100 × 1.6 ×10-19 joule. This is lost when electron moves through a distance d towards the negative plate.

K.E. = work done = qE × s

$\displaystyle K.E = e (\frac{\sigma}{\epsilon_0}) d$ ; Where σ = surface charge dinsity .

$\displaystyle d = \frac{K.E \times \epsilon_0}{e \times \sigma}$

$\displaystyle d = \frac{100\times 1.6 \times 10^{-19}\times 8.85 \times 10^{-12}}{1.6 \times 10^{-19} \times 2 \times 10^{-6}}$

= 4.43 × 10-4 m

= 0.44 mm

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