Question

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2-V_1=120V.$ (i.e. plate $2$ is at a higher potential). The plates are separated by $d=0.1m$ 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 $2$? $(e=1.6\times {10}^{-19}C,m_e=9.11\times {10}^{-31}kg)$

• A. $32\times {10}^{-19}m/s$
• B. $6.49\times {10}^{6}m/s$
• C. $7.02\times {10}^{12}m/s$
• D. $1.87\times {10}^{6}m/s$

Answer 1

Answer: (B)

$6.49\times {10}^{6}m/s$

According to energy conservation, potential energy of electron is converted into kinetic energy

thus, $eV=\frac{1}{2}m{v}^2$

or $v=\sqrt{\frac{2eV}{m}}=\sqrt{\frac{2\times 1.6\times {10}^{-19}\times 120}{9.11\times {10}^{-31}}}=6.49\times {10}^{6}m/s$