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Electrostatic Force Field “If there is onethey have to come (or go)!” Pre-presentation Self Assessment Activity Your comfort level with your responses to the following two question assessment tool should indicate if the presentation that follows will increase you knowledge base on the topic outlined by the questions in this tool. “If there is one- they have to come (or go)!” Pre-presentation Self Assessment Activity Problem #1: Using the reference graphic shown below, develop a model that will predict the coordinate position when the electron is exiting the electrostatic field. (Assume that the electron’s horizontal velocity has a constant value while the electron is in the electrostatic field. Also assume that “d” is the distance between the two charged plates.) +z ux 0 Va e- y L x Vb -z + the horizontal length of the electrostatic field. “If there is one- they have to come (or go)!” Pre-presentation Self Assessment Activity Problem #2: Using your answer from review problem #1, develop the model equation that will predict the electric field needed to have the electron collide with the upper charged plate just as the electron is leaving the electric field. +z ux 0 Va e- y L x Vb -z + the horizontal length of the electrostatic field. Electric force field and the resultant motion “If there is one- electrons have to come (or go)!” When a force exists where it exists is called a force field For engineers and technicians it is usually very convenient to describe the force field instead of the force. “If there is one- they have to come (or go)!” Electric Field between two charged Plates Magnitude of Electric field strength Electric field strength vector [ E= [ -1 E= (4peo) (q1) V R 2 1,2 d ] Newton/Coulomb ] Volts/meters By historic definition, voltage change occurs because positive charge moves from higher energy environment to lower energy environment. z ( )= V = Vb - Va where Vb dv is the sum of all of the infinitesimal voltage changes as the positive test charge moves from Va to Vb. Va + - felectric felectric f dl x y dv ] (q) = - [dv/dl] (q) = = -[ E - [dv] (q) As the charge moves an infinitesimal distance in the electrostatic field the voltage value changes an infinitesimal amount. dv = -( 1 q ) f dl dv = -( f ) q q= edv = ( E ) dl dl “If there is one- they have to come (or go)!” Electron in an Electrostatic Field Change in velocity Change in time if an electron is accelerating then its velocity is changing all the time. du = a dt x x electron accelerates along the “x” direction toward positive plate Newton’s model as developed for distance traveled by an object with mass in a uniform gravitational force field. (same or opposite direction as field lines) x= z E Vb 2 2 a x t + u0 t + x 0 This acceleration term is for the acceleration of gravity Va e- Distance traveled model for electron moving in the x direction in a uniform electrostatic force field. + - 1 x= 1 2 2 a x t + u0 t + x 0 x y This acceleration term is for the acceleration of the electron in the electrostatic field. “If there is one- they have to come (or go)!” Electron in Electrostatic Field Newton discovered that in a gravitational field the force (the objects weight) was proportional to the objects mass. force m Gravitational force = a x m electron accelerates along the “x” direction toward positive plate mass of the object This acceleration term is constant as long as the gravitational field strength is constant. z Since both gravitational and electrostatic forces follow an inverse square distance relationship, by analogy: E Vb Electrostatic force = ax me Va e- + - This acceleration term is constant as long as the electrostatic field strength is constant. Electrostatic force = E q E q = ax m e x ax = charge to mass ratio y mass of the electron q m ( )E “If there is one- they have to come (or go)!” Electron in Electrostatic Field Electrostatic force = ax me mass of the electron This acceleration term is constant as long as the electrostatic field strength is constant. electron accelerates along the “x” direction toward positive plate electron velocity in the x direction of the electric field. z E Vb x = + - ( q E t +u m 0 ) current position of electron in “x” direction when the electron started at negative plate. Va e- ux = t2 [( t1 q E t +u m 0 ) ] dt (When t = 0) 1 x 1 x = 2 y ( 2 q E t + u t 0+x 0 m ) “If there is one- they have to come (or go)!” Electron in Electrostatic Field Typical situation: An electron in a vacuum environment has a constant velocity, ux , in the x direction and is about to enter an electrostatic field as shown below. +z ux 0 Va e- + y x Vb -z What is the predicted path of the electron as it travels through the electric field if the horizontal velocity, ux, remains constant? “If there is one- they have to come (or go)!” In this situation, the electron will be directed up (in the +Z direction) as it moves through the electric field in the X direction. Electron in Electrostatic Field Typical situation: An electron in a vacuum environment has a constant velocity, ux , in the x direction and is about to enter an electrostatic field as shown below. +z ux 0 Va e- + e- Electron distance traveled in the Z direction as a function of the time the electron is in the electric field. z = 1 2 ( 2 q E t + u t 0+z m ) 0 y x Vb -z What is the exact path the electron will travel as it goes through the electric field? From the co-ordinate system for this situation: z = 0 0 1 z = 2 ( 2 q E t + u t0 m ) Note: Setting zo = 0 allows the model to follow the position of the electron as it enters half way between the top and the bottom charged plates. “If there is one- they have to come (or go)!” In this case, while the electron is in the electric field it will move in the up (+z) while it moves to the right. Electron in Electrostatic Field Typical situation: An electron in a vacuum environment has a constant velocity, ux , in the x direction and is about to enter an electrostatic field as shown below. +z ux 0 Va e- A) Model for upward motion. 1 +z z = = 2 ( 2 q E t + u t0 m ) B) Model for motion to the right. + ux = a constant value = u0 y x Vb -z What is the exact path the electron will travel as it goes through the electric field? x = t2 t1 (u0) dt Electron distance traveled in the “x” direction. x = u0 t When t1 =0 “If there is one- they have to come (or go)!” In this case, while the electron is in the electric field it will move in the up (+z) while it moves to the right. Electron in Electrostatic Field Typical situation: An electron in a vacuum environment has a constant velocity, ux , in the x direction and is about to enter an electrostatic field as shown below. 0 Travel upward. 1 +z z = = 2 +z ux C) Model for combined motion. Va e- + ( 2 q E t + u t0 m ) Travel to the right. y x Vb -z What is the exact path the electron will travel as it goes through the electric field? x = u0 t or t = x u0 Actual (x,z) position of electron as a function of time z - (t)= 1 e 2 ( q E m When t0 = 0 x 2 ) ( u0) “If there is one- they have to come (or go)!” Electron in Electrostatic Field z - (t)= 1 e 2 q E m ( ux 0 (remember that for constant speed in the x direction, x = u0? t ) time “x” position +z Va t in sec + y e- x = u0 t “z” position 2 z(x)= [ q E ]x 2mu0 2 x Vb -z 1 2 )( ) Typical situation: An electron in a vacuum environment has a constant velocity, ux , in the x direction and is about to enter an electrostatic field as shown below. x u0 2 3 Time (seconds) 4 t0 =0 x 0= u 0 t 0 =0 z(x)= K( u x )= 0 0 0 2 t1 =1 x1 = u 0 (1) 2 z(x)=K(u 0 1) =1 u 0 K t2 =2 x2 = u 0 (2) 2 z(x)=K(u 0 2) =4 u 0 K t3 =3 x3 = u 0 (3) 2 z(x)=K(u 0 3) =9 u 0 K 2 2 Note: K= ( qE 2 mu 0 ) “If there is one- they have to come (or go)!” Electron in Electrostatic Field ( z - (t)= 1 e 2 q E m x u0 )( ) Typical situation: (remember that for constant speed in the x direction, x = u0? t ) +z 2 Ku 0 0 2 Va t in sec + y e- x u0 Vb -z 1 2 3 Time (seconds) 4 x u0 z(x) 2 Ku 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 4 9 16 25 36 t t t 2 qE 2 mu 0 ) Note: K= ( “If there is one- they have to come (or go)!” Electron in Electrostatic Field ( z - (t)= 1 e 2 q E m x u0 2 )( ) Typical situation: The data indicates a parabolic path t in sec +z 2 Ku 0 0 Va + y e- x u0 Vb -z 1 2 x u0 Time (seconds) 4 2 Ku 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 4 9 16 25 36 t t t 2 qE 2 mu 0 ) Note: 3 z(x) K= ( “If there is one- they have to come (or go)!” Electron in Electrostatic Field Note: Vd E=( d ) Vd = Vb - V a The data indicates a parabolic path d is the distance between the two charged plates. +z 2 Ku 0 Va + e- y x u0 0 Vb -z 1 2 3 Time (seconds) 4 t in sec x u0 z(x) 2 Ku 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 4 9 16 25 36 t t t 2 2 1 q 1 V d z(x)= ( )( x) ) ( )( ) ( m u0 2 d “If there is one- they have to come (or go)!” Pre-presentation Self Assessment Activity Problem #1: Using the reference graphic shown below, develop a model that will predict the coordinate position when the electron is exiting the electrostatic field. Assume that the electron’s horizontal velocity has a constant value while the electron is in the electrostatic field. Also assume that “d” is the distance between the two charged plates. +z ux 0 Va e- y + L x Vb -z Write your answer down before you proceed. the horizontal length of the electrostatic field. “If there is one- they have to come (or go)!” Post-Presentation Self Assessment Activity Problem #1: Using the reference graphic shown below, develop a model that will predict the coordinate position when the electron is exiting the electrostatic field. Assume that the electron’s horizontal velocity has a constant value while the electron is in the electrostatic field. Also assume that “d” is the distance between the two charged plates. +z ux 0 Va e- y ( + ) ( Vdd) x 1 u0 2 ( )(L) L Vb -z 1 q z(x)= ( ) m 2 the horizontal length of the electrostatic field. “If there is one- they have to come (or go)!” Post-Presentation Self Assessment Activity Problem #2: Using your answer from review problem #1, develop the model equation that will predict the electric field needed to have the electron collide with the upper charged plate just as the electron is leaving the electric field. +z ux 0 Va e- y + )( Vd q m) d ( ) 2 1 ( u )(L) 0 L x Vb -z z(x)= ( 1 2 the horizontal length of the electrostatic field. “If there is one- they have to come (or go)!” Post-Presentation Self Assessment Activity Problem #2: Using your answer from review problem #1, develop the model equation that will predict the electric field needed to have the electron collide with the upper charged plate just as the electron is leaving the electric field. +z ux 0 Va e- y z(x)= ( + 1 2 )( Vd q m) d ( ) 2 1 ( u )(L) 0 L x Vb -z Write your answer down before you proceed. the horizontal length of the electrostatic field. “If there is one- they have to come (or go)!” Post-Presentation Self Assessment Activity Problem #2: Using your answer from review problem #1, develop the model equation that will predict the electric field needed to have the electron collide with the upper charged plate just as the electron is leaving the electric field. +z ux 0 Va e- y z(x)= ( + 1 2 )( Vd q m) d ( ) 2 1 ( u )(L) 0 L x the horizontal length of the electrostatic field. Vb 2 1 q 1 -z = z(x) ( )( L) ( ) ) ( ) ( m u0 2 Since the distance “d” between the d Vd plates is fixed the only variable available is the electric field strength. [ -1 ] “If there is one- they have to come (or go)!” Post-Presentation Self Assessment Activity Problem #2: Using your answer from review problem #1, develop the model equation that will predict the electric field needed to have the electron collide with the upper charged plate just as the electron is leaving the electric field. +z ux 0 Va e- + y L d x Note: The charge, “q”, on a -19 Coulomb single electron =1.6 x10 The mass, “m”, of a -31 kg single electron =9.1 x10 d = 2 Vd ( )= d [ 9.1 d u0 2 1.6 L -1 ] the horizontal length of the electrostatic field. Vb -z 2 1 q 1 ( 2 )( m )( u )(L) 0 ( ) ( )[ Vd ] x 10 -12 “If there is one- they have to come (or go)!” End of Presentation Things to really remember: 1) The definition of E including its units. 2) The name for E. 3) The direction of E. 4) The charge (in Coulomb) on a single electron. 5) The unit of force in an electrostatic field. Run this presentation over (and over) until you at least remember these 5 things. End of Presentation