Question

Two parallel plates 5cm apart are connected to a 500 V D.C supply. Assuming that an electron starts from rest, its velocity after a nano second is

• A. $1.56\times {10}^{6}m/s$
• B. $1.66\times {10}^{6}m/s$
• C. $1.76\times {10}^{6}m/s$
• D. $1.86\times {10}^{6}m/s$

Answer 1

The correct option is C $1.76\times {10}^{6}m/s$

Electric field in the parallel plates $=\frac{500}{5}\times 100N/e$

${10}^{4}N/c$
Force experienced by electron $=e{10}^4$

Acceleration $=\frac{e{10}^4}{m}={10}^4\times 1.76\times {10}^{11}=1.76\times {10}^{15}$ [ $\frac{e}{m}$ ratio is known ]

So,
Velocity after ${10}^{-9}$ seconds,
$V=v+at[v=0]$
$V=1.76\times {10}^{15}\times {10}^{-9}m/s$
$V=1.76\times {10}^{6}m/s$
$V=1.76\times {10}^{6}m/s$
So, the answer is option (C).