An electron is moving with speed of 1 m/s at distance of 1 m from a large sheet of charge with density sC/m2. Find maximum value ofs such that electron hit the sheet after 1 sec. (mass of electron 9 * 10–31 kg, permittivity of free space e0 = 9 * 10–12C2/Nm2)

For maximum value of s, initially, electron must move away from plate. ut + 1 2 at2 = s t = 1u = 1m/s s = –1 m 1 * 1 – 1 2 a * 12 = – 1 -> a = 4m/s2 q E m = 4 q σ 2 ε 0 m = 4 σ = 4 * 2 * 9 * 1 0 − 1 2 * 9 * 1 0 − 3 1 1 . 6 * 1 0 − 1 9 = 8 * 8 1 1 . 6 * 1 0 − 2 4 = 4.05 * 10–22C/m2

An electron is moving with speed of 1 m/s at distance of 1 m from a large sheet of charge with density sC/m². Find maximum value ofs such that electron hit the sheet after 1 sec.

**(mass of electron 9 * 10^–31 kg, permittivity of free space e₀ = 9 * 10^–12C²/Nm²)**

Option 1 - 4.05 × 10–22 C/m2

Option 2 - 8.1 × 10–22 C/m2

Option 3 - 4.05 × 1024 C/m2

Option 4 - 2.02 × 10–20 C/m2

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Answered by

Alok Kumar Singh | Contributor-Level 10

4 months ago

Correct Option - 1

Detailed Solution:

For maximum value of s, initially, electron must move away from plate.

ut + $\frac{1}{2}$ at² = s

t = 1u = 1m/s s = –1 m

1 * 1 – $\frac{1}{2}$ a * 1² = – 1

-> a = 4m/s²

$\frac{q E}{m} = 4$

$\frac{q σ}{2 ε_{0} m} = 4$

$σ = \frac{4 * 2 * 9 * 1 0^{- 12} * 9 * 1 0^{- 31}}{1.6 * 1 0^{- 19}}$

$= \frac{8 * 81}{1.6} * 1 0^{- 24}$

= 4.05 * 10^–22C/m²

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