Respuesta :
Answer:
t=89.44 sec
Explanation:
Given that
d= 100 m
Mass of electron
[tex]m=9.11\times 10^{-31}kg[/tex]
Force acting on electron
[tex]F=\dfrac{Kq^2}{d^2}[/tex]
Now by putting the values of K and charge on electron
[tex]F=\dfrac{Kq^2}{d^2}[/tex]
[tex]F=\dfrac{9\times 10^9(1.6\times 10^{-19})^2}{100^2}[/tex]
[tex]F=2.3\times 10^{-32}[/tex]
As we know that
F= m a
So acceleration of electron
a=F/m
[tex]a=\dfrac{2.3\times 10^{-32}}{9.11\times 10^{-31}}\ m/s^2[/tex]
[tex]a=0.025\ m/s^2[/tex]
We know that
[tex]S=ut+\dfrac{1}{2}at^2[/tex]
here electron move from rest so u= 0
[tex]100=\dfrac{1}{2}\times 0.025^2\times t^2[/tex]
t=89.44 sec
So time taken by electron is 89.44 sec.
Force on electron, released from rest at a distance from conducting plane indirectly proportional to this distance coulombs law. Time required for electron to strike the plane is 89.44 seconds.
What is coulombs law?
Coulombs law states the the force of attraction or repulsion between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of distance between them.
It can be given as,
[tex]F=k\dfrac{q_1q_2}{r^2}[/tex]
Here, [tex]k[/tex] is coulombs constant.
Given information-
The electron is released from rest at a distance 100 m from an infinite conducting plane.
The acceleration of a object is the ratio of force applied on it to the mass of the object. Thus the acceleration of the electron is,
[tex]a=\dfrac{F}{m}[/tex]
Force is the ratio of charge on particles and the square of distance between them, multiplied by coulomb's constant. Thus,
[tex]a=\dfrac{k\dfrac{q_1q_2}{r^2}}{m}\\a=\dfrac{k{q_1q_2}}{m{r^2}}[/tex]
As the mass of the electron is [tex]9.11\times10^{-31}kg[/tex] and the charge on a electron is [tex]1.6\times10^{-19} C[/tex]. Thus put the value in above expression as,
[tex]a=\dfrac{(9\times10^9)(1.6\times10^{-19})(1.6\times10^{-19})}{9.11\times10^{-31}\times100^2}\\a=0.025\rm m/s^2[/tex]
As the value of acceleration is 0.025 meter per second squared and initial velocity is zero. Thus by the distance formula of equation of motion,
[tex]100=0+\dfrac{1}{2}\times0.025\times t^2\\t=89.44 \rm sec[/tex]
Therefore, the time required for the electron to strike the plane is 89.44 seconds.
Learn more about the coulombs law here;
https://brainly.com/question/506926
