Q117 / 150 · JEE Main 2006 · Physics

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2-V_1=20 \mathrm{~V}$. (i.e. plate 2 is at a higher potential). The plates are separated by $d=0.1 \mathrm{~m}$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1 . What is its speed when it hits plate $2 ?$ $\left(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}, \mathrm{m}_{\mathrm{e}}=9.11 \times 10^{-31} \mathrm{~kg}\right)$ Figure

  • A
    $32 \times 10^{-19} \mathrm{~m} / \mathrm{s}$
  • Correct answer
    B
    $2.65 \times 10^6 \mathrm{~m} / \mathrm{s}$
  • C
    $7.02 \times 10^{12} \mathrm{~m} / \mathrm{s}$
  • D
    $1.87 \times 10^6 \mathrm{~m} / \mathrm{s}$

Solution

$\frac{1}{2} \mathrm{mv}^2=\mathrm{eV}$ $\mathrm{v}=\sqrt{\frac{2 \mathrm{eV}}{\mathrm{m}}}=2.65 \times 10^6 \mathrm{~m} / \mathrm{s}$

Hence, the correct answer is option: 'B'.

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