Physics_Electricity & Magnetism_Motion of Charged Particle in E FieldMOTION OF CHARGED PARTICLE IN E FIELDL.O1. Solve problems involving the use ofV q W =.2. Convert energy from joules into electron volts and vise versa.3. Derive the epression dVE=for the magnitude of the electric field !a"ay from the edges# bet"een t"o oppositely charged parallel plates a distance d apart$ "here %& is the potential difference bet"een the plates.'. Solve problems involving the use ofdVE= .Electric Potential (V)(he energy re)uired to bring a !*ve# unit electric charge from infinity to the point in an electric field at "hich the potential is being specified. specified point infinity Potential Difference (V)(he potential difference bet"een 2 points in an electric field or circuit is the difference in values of the electric potentials at the2 points i.e. it is the "or+ done in moving a unit charge from one point of the E field,circuit to the other.-.d. bet"een t"o points in an . field/a#01

E%& 2 &0 3 &1-.d. bet"een 2 points in a circuit/b#10%& 2 &0 3 &1 (he e)uation for potential difference/1Physics_Electricity & Magnetism_Motion of Charged Particle in E FieldqWV = 4here$%& 2 potential difference4 2 "or+ done) 2 chargeThe electron-volt unit1 unit of energy e)ual to the "or+ done on an electron in moving it through a potential difference of one volt.1 e& 2 1.516718 9 (1.516718# !1.516718#Deriving equation for EConsider 2 points !: ; d4here/4 2 "or+ done> 2 force d 2 distance travel0ut in an electric field$ the force acting on a charge "ould be/29 e&* ** * ** *7 777 777Physics_Electricity & Magnetism_Motion of Charged Particle in E Field> 2 .)So then combining both definition of "or+ "e obtain/)%& 2 .)d%& 2 .d?ence/dVE="here/. 2 electric field %& 2 potential differenced 2 distance traveled.g?o" much "or+ is re)uired to move a charge of *@AC across apotential difference of 1B6&CD1ns"erE 1.6B16739F L.O3Physics_Electricity & Magnetism_Motion of Charged Particle in E Field1. Describe the motion of a charged particle in a uniform electric field.2. -erform calculations involving the movement of charged particles parallel and anti7parallel to a uniform electric field.Charges moving parallel to the fieldCharges moving anti-parallel to field

(he force eperienced by the charged particle due to the field is/Eq=4here/> 2 force. 2 electric field strength) 2 charge of the particle0ecause the particle eperiences a force from the electric field$ it "ill also eperience acceleration.> 2 ma 2 .)?ence/mEqa ="here/a 2 acceleration. 2 electric field strength) 2 charge of particlem 2 mass of particle1s long as the charged particle is in the electric field$ it "ill eperience a constant force !as long as the electric field stays 'Physics_Electricity & Magnetism_Motion of Charged Particle in E Fieldconstant# that gives it a constant acceleration. ?ence$ "e can apply the e)uations of movement to describe ho" the particle moves in the filed.v 2 u * ats 2 ut * 21at2v2 2 u2 * 2as4here/v 2 final velocityu 2 initial velocitya 2 acceleration due to electric fieldt 2 time ta+ens 2 distance traveled>ormulae for a *ve charge moving parallel to the field/>ormulae for a 3ve charge moving parallel to the field/>ormulae for a *ve charge moving anti7parallel to the field/B132Physics_Electricity & Magnetism_Motion of Charged Particle in E Field >ormulae for a 3ve charge moving anti7parallel to the field/.g1 266e& electron passes through a hole in a screen into a region "here there is a uniform electric field of G66HC71.!1# 4hat "as the initial speed of the electronC!2# If the initial velocity is in the direction of the field$ ho" far does the electron travel before it reverses its direction of motionCD1E !1# G.3G165ms71/ !2# 6.2BmFL.O5Physics_Electricity & Magnetism_Motion of Charged Particle in E Field1. Compare the motion of a projectile in the absence of air resistance "ith the motion of a charged particle in a uniform electric field.2. Calculate the time of flight and the deflection of a charged particle that enters a uniform electric field at right angles tothe field.Jotion of charged particle perpendicular to E fieldEJotion of a projectile !"ithout air resistance#/Jotion of a *ve ; a 7ve charged particle in a uniform electric field/.g@Physics_Electricity & Magnetism_Motion of Charged Particle in E Field1 uniform electric field of intensity 2.6616'&m71 is set up bet"een t"o parallel horiKontal plates of length 'cm. the lo"erplate is at positive potential relative to the upper. 1n electron$ "ith initial velocity of 2.6616@ms71$ is projected horiKontally along an ais mid7"ay bet"een the t"o plates. Calculate/!1# (he acceleration of the electron "hile it is in the field/!2# (he time it ta+es for the electron to traverse the field/!3# ?o" far do"n the electron has moved "hen it reaches the end of the plates/!'# (he vertical velocity of the electron on leaving the plates/!B# (he final velocity of the electron on leaving the region bet"een the plates.D1E !1# 3.B1161Bms72/ !2# 2.661678s$ !3# @.63mm/!'# @.63165ms71$ do"n/ !B# 2.1216@ms71$ at 18.'L belo" horiKontal.FDWor!ing spaceFL.OGPhysics_Electricity & Magnetism_Motion of Charged Particle in E Field1. Describe ho" hydrogen atoms can be given a negative charge or a positive charge in an ion source of a cyclotron.2. Describe the follo"ing parts of a cyclotronE 7Semicircular metal containers !MdeesN#. 7.vacuated outer container.3. .plain "hy there is no electric field inside the dees.C"clotron 1 cyclic particle accelerator in "hich charged particles fed intothe center of the device are accelerated in an out"ard spiral path inside t"o hollo" D7shaped conductors placed to form a split circle. 1 magnetic field is applied at right7angles to the plane of the dees !to ma+e them follo" curved,circular paths# and an alternating potential difference is applied bet"een them.(he fre)uency of the alternating potential difference is arranged so that the particles are accelerated each time they reach the evacuated gap bet"een the dees. #on sourceCreates,-roduces *ve or 7ve ions for acceleration.(o create positive hydrogen ionsE (he ion source in a cyclotron is usually a heated "ire "here hydrogen atoms gain energy by interacting "ith the "ire$ becoming ecited and eventually ionised "here the electron escapes leaving the proton !nucleus# hence a positive ion.(o create negtive hydrogen ionsE(he ?7 ions used for acceleration are obtained from ?ydrogen gas. (he gas is pumped into a chamber "here it is heated by passing a large current of electrons through it. On passing through the chamber$ the electrons collide "ith the ?ydrogen gas$ producing a large number of ?7 ions. (he ?7 ions are then injected into the vacuum chamber by the application of anothervoltage. 1 large collection of ions injected into the accelerating chamber forms an ion beam$ other"ise +no"n as the cyclotron beam.$emicircular metal containers (dees)?ollo" semi7cylindrical metal chambers/ opened at the diameter. (hey are called dees because of their shape.0ecause the dees are hollo"$ there is no . field inside the dees/all charges are on the surface of the conductor.L.O.8Physics_Electricity & Magnetism_Motion of Charged Particle in E Field1. Describe ho" an electric field bet"een the dees can transfer energy to an ion passing bet"een them.2. Describe ho" ions could be accelerated to high energies if they could be made to move in a circular path in side the dees so that they repeatedly move across the electric field$ the direction of "hich "as reversing every half7revolution.3. Calculate the energy transferred to an ion each time it passes bet"een the dees.'. .plain "hy the cyclotron must be evacuated.(he dees act as t"o parallel plates !or electrodes# to accelerate the ions from one dee to another.(he ion gets accelerated across a potential difference !that alternates according to the 1C# and the "or+ done to acceleratethe ion is transformed into +inetic energy !hence "e say the ionhas gained +inetic energy#/16Physics_Electricity & Magnetism_Motion of Charged Particle in E Field(he process continues as the ions reverse direction inside the dees and re7enter the gap bet"een the dees !"here the . field ispresent# and are accelerated to high energies !meaning high +inetic energy since the velocity "ould be huge#..ach time an ion passes through the gap bet"een the dees$ "or+ is turned into +inetic energyE% W =221mv V q = Evacuated &uter Container'Tan!(he entire components are contained in the vacuum chamber. (he accelerated ions "ill not lose any of its +inetic energy through collisions "ith air molecules.11Physics_Electricity & Magnetism_Motion of Charged Particle in E Field!"MMAR#1 E$e%tri% Potenti$ Di&&eren%e(he electric potential differenceV bet"een t"o points is the "or+ W done per unit charge q on a small positive test charge moved bet"een the points$ provided that all other charges remainundisturbedEV 2 W,q((he unit of potential difference$ the volt !$ is e)ual to a joule per coulomb !9 CO1#.(he electronvolt !e is the "or+ done "hen a charge of one electron moves through a potential difference of 1 &.2 A%%e$ertion inConstnt E$e%tri% Fie$d(he force on a charged particle moving in a uniform electric field is constant in magnitude and direction$ thus producing a constant acceleration.3 Motion o&Chrged Prti%$e inConstnt E$e%tri% Fie$d4hen a charged particle moves across a uniform electric field the component of the velocity perpendicular to the field remains constant.12