Question

In the uniform electric field of $E = 1 \times 10^4 NC ^{-1}$, an electron is accelerated from rest. The velocity (in $m\,s^{-1})$ of the electron when it has travelled a distance of $2 \times 10^{-2}$ m is nearly $(\frac {e}{m}$of electron $= \,1.8 \times 10^{11} C\,kg^{-1})$

• A. $1.6\times10^{6}\,ms^{-1}$
• B. $0.85\times10^{6}\, ms^{-1}$
• C. $0.425 \times10^{6}\,ms^{-1}$
• D. $8.5 \times 10^{6}\,ms^{-1}$

Answer 1

Answer: (D)

By work-energy theorem,
Work done by electric field = Change in KE of electron
or $qE \,x=\frac{1}{2} m v^{2}$
or $v =\sqrt{\frac{2 q E x}{m}}$
$=\sqrt{2 \times 1.8 \times 10^{11} \times 1 \times 10^{4} \times 2 \times 10^{-2}} $
$=8.5 \times 10^{6} \,ms ^{-1}$