an electron is projected horizontally at a speed of 3x10^6 m/s into a uniform electric field 200 N/C produced by two charged plates of width 0.1m (a) find the a cceleration of the electron in the elec field.(b) finn the time takes to travel through the electric field.(c) what is the vertical displacement of the electron in the electric field(d) find the speed of the electron as it images from the field
To find the answers to the given questions, we can use some physics equations and principles. Let's break down each question and explain how to get the answers step by step:
(a) Find the acceleration of the electron in the electric field:
The force experienced by the electron in the electric field can be calculated using the equation: F = qE,
where F is the force, q is the charge of the electron, and E is the electric field strength.
Since the electron has a negative charge, the force will act in the opposite direction of the electric field, so the equation becomes: F = -qE.
The acceleration of the electron can be found using Newton's second law: F = ma,
where m is the mass of the electron and a is the acceleration.
By substituting the force equation into Newton's second law, we get: -qE = ma,
which allows us to solve for the acceleration: a = -qE/m.
Given:
- q = charge of the electron = -1.6 x 10^-19 C (Coulombs)
- E = electric field strength = 200 N/C (Newtons per Coulomb)
- m = mass of the electron = 9.1 x 10^-31 kg
Substitute the values into the equation: a = (-1.6 x 10^-19 C)(200 N/C) / (9.1 x 10^-31 kg)
Calculate the acceleration to get the answer.
(b) Find the time it takes to travel through the electric field:
Since the electron is projected horizontally, the electric field only affects the vertical motion and not the horizontal motion. Therefore, the initial horizontal velocity remains constant throughout.
The time taken to travel through the electric field can be calculated using the equation: t = d/v,
where t is the time, d is the vertical distance traveled, and v is the initial vertical velocity.
The initial vertical velocity (vy) of the electron can be found using the equation: vy = a*t,
where a is the acceleration calculated in part (a) and t is the time taken to travel through the electric field.
Since the electron starts with zero initial vertical velocity (vy), we can set up the equation: 0 = a*t,
and solve for t to get the time.
(c) Find the vertical displacement of the electron in the electric field:
The vertical displacement (d) can be calculated using the equation: d = 0.5*a*t²,
where a is the acceleration calculated in part (a) and t is the time taken to travel through the electric field.
Substitute the values into the equation to calculate the vertical displacement.
(d) Find the speed of the electron as it emerges from the field:
The final speed of the electron as it emerges from the field can be calculated using the equation: vf = vi + at,
where vi is the initial vertical velocity and vf is the final vertical velocity.
Since the electron starts with zero initial vertical velocity (vi), we can set up the equation: vf = 0 + at,
and solve for vf to get the final speed.
I hope this helps you in solving the problem!