Answer:
The velocity of electron is 592999.45 m/s.
Explanation:
Given that,
Electric field = 1000 V/m
Distance = 0.10 cm
(a).We need to calculate the velocity of electron
Using newton's law
[tex]F=qE[/tex]
[tex]ma=qE[/tex]...(I)
Now, Using equation of motion
[tex]v^2=u^2+2as[/tex]
[tex]a=\dfrac{v^2}{2s}[/tex]
Put the value of a in equation (I)
[tex]qE=m\times\dfrac{v^2}{2s}[/tex]
[tex]v=\sqrt{\dfrac{2sqE}{m}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{2\times0.10\times10^{-2}\times1.6\times10^{-19}\times1000}{9.1\times10^{-31}}}[/tex]
[tex]v=592999.45\ m/s[/tex]
(b). We need to calculate the velocity of electron
Using work theorem
[tex]\text{work done by all forces}=\text{change in kinetic energy}[/tex]
[tex](qE+mg)\times d=\dfrac{1}{2}mv^2[/tex]
Here, weight of electron is very less compare to electric field
So, neglect to weight of electron.
[tex]qE\times d=\dfrac{1}{2}mv^2[/tex]
[tex]v=\sqrt{\dfrac{2qE\times d}{m}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{2\times1.6\times10^{-19}\times1000\times0.10\times10^{-2}}{9.1\times10^{-31}}}[/tex]
[tex]v=592999.45\ m/s[/tex]
Hence, The velocity of electron is 592999.45 m/s.
