Question

Two insulating plates, both uniformly charged in such a way that the potential difference between them is $V_2-V_1=20\text{V}$. The plates are separated by $d=0.1\text{m}$ 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 the plate $2$?

$[e=1.6\times {10}^{-19}\text{C}$ and $m_e=9\times {10}^{-31}\text{kg}]$

• A. $2.7\times {10}^6\text{m}/\text{s}$
• B. $1.8\times {10}^6\text{m}/\text{s}$
• C. $1.6\times {10}^6\text{m}/\text{s}$
• D. $1.2\times {10}^6\text{m}/\text{s}$

Answer 1

The correct option is A $2.7\times {10}^6\text{m}/\text{s}$

Given, potential difference between the plates is, $V=V_2-V_1=20\text{V}$

From work-energy theorem,

Work done by all the forces $=$ charge in KE

$\Rightarrow eV=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$\Rightarrow eV=\frac{1}{2}m{v}^2-0$

$\Rightarrow v=\sqrt{\frac{2eV}{m}}=\sqrt{\frac{2\times 1.6\times {10}^{-19}\times 20}{9\times {10}^{-31}}}$

$\Rightarrow v=2.7\times {10}^6\text{m}/\text{s}$