University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2023
Views:

494

Pages:

6
Author:

Dixie Summers

Motion of a Charged Particle in a Uniform Electric Field charged particle in electric field experiences force, and if it is free to move, an acceleration. if the only force is due to the electric field  F  ma  qE. E is constant - - - - - - - - - - - - - - F E + + + + + + + + + + + + + a constant, use the equations of kinematics (Physics 101). Make sure you understand what a uniform electric field is. Example: an electron moving with velocity v0 in the positive x direction enters a region of uniform electric field that makes a right angle with the electron’s initial velocity. Express the position and velocity of the electron as a function of time. y - - - - - - - - - - - - - x -e v0 E + + + + + + + + + + + + + vfx  vix  a x t 1 2 x f  x i  vix t  a x  t  2 Express the position and velocity of the electron as a function of time. FE = qE =  -e  E = -eEjˆ = ma y -e v0 FE a E x eE ˆ a=j m ax = 0 eE ay = m Let’s work the rest of the problem one component at a time. Express the position and velocity of the electron as a function of time. eE ay = m ax = 0 y 0 -e v0 FE a E x 1 2 x = x i + vix t + a x t 2 x = v0 t 0 0 1 2 y = y i + v iy t + a y t 2 Position: x = v0 t 0 1 eE 2 y=t 2 m y= 1 2 1 eE 2 a yt = t 2 2 m Express the position and velocity of the electron as a function of time. eE ay = m ax = 0 y 0 -e v0 FE a E x v x = vix + a x t vx = v0 0 v y = viy + a y t Velocity: v x = v0 eE vy = - t m v y = a y t= - eE t m What is the shape of the electron’s path? y -e x = v0 t v0 FE a E x y=- 1 eE 2 t 2 m x t= v0 2  1 eE  2 1 eE  x  y=x   = - 2  2 m  v0   2 mv 0  The trajectory of the electron is a parabola, concave down. Just like the trajectory of a ball thrown horizontally in the gravitational field of the Earth. Quiz: What would be different for a proton?