Electron Ballistics in Electric and Magnetic Fields

1. BE-II SEMESTER ADVANCED PHYSICS UNIT-II ELECTRON BALLISTICS DEPARTMENT OF APPLIED PHYSICS

2. SYLLABUS • Introduction, Motion of charged particle in parallel & perpendicular electric Field • Motion of charged particle Inclined electric Field, electrostatic deflection • Motion of charged particles in parallel & perpendicular magnetic fields, • Motion of charged particles in projected magnetic fields, magnetostatic deflection • Cross electric and magnetic field Configuration , Velocity Filter

3. q r Q Basic Definitions • Electric Charge:- Any particle or object that establishes an electric field. • Coulomb Force:-The force of interaction between two point charges Q1 and Q2 • Electric field/ Electric field strength/ Intensity:- The electric force F experienced by a unit positive test charge

4. Electric potential (V):- • Electron-volt :- The electron-volt is an amount of energy acquired by an electron accelerated through a potential of one volt. 1 electron-volt =1.6 x 10-19 J

5. - V + P Q X O d I] Motion of electron parallel to uniform electric field : The potential along OX rises uniformly from zero to ‘V’ volts between the plates so that a constant potential gradient

6. An electron will be acted upon by a constant force • F = -eE • (-ive sign indicate that force is opposite to electric field.) • The acceleration is given by • The equations of kinematics in one dimension are given as

7. Taking and substituting for ‘a’, we get • The Kinetic Energy of the electron after moving through a distance ‘x’ in the field is • As Ex = V, K.E.= eV therefore,

8. II] Motion of electron perpendicular to uniform electric field : l A + + + + + + + + + + + v0 y d X - - - - - - - - - - - B _ _ • Horizontal velocity component vx remains unchanged • However it is continuously attracted towards the plate A and attains velocity vy. • The electron will move in a straight line with a resultant velocity having components vx & vy .

9. The velocity attained by the electron at any time ‘t’ is Due to uniform electric field E, a constant force F= eE and a constant acceleration • Hence the displacement ‘y’ of an electron in time t is obtained by is dragging the electron upwards.

10. Transit time • Eliminating ‘t’ from the equation of ‘y’ we get Where k is constant = • This equation shows that the path of electron entering in uniform electric field at right angles to the field lines and traveling through the field is parabolic.

11. Electrostatic Deflection Region I Region II Region III P + + + + + + + + + + + + + vx M D y θ e Q o N Electron gun - - - - - - - - - - - - - - - - - - - - - - l L vy d • Slope of line OP= • From fig. D=L tanθ : screen

12. l is the length of plate deflecting plate; • L is the length of the screen from centre of the deflecting plate • d is the distance between deflecting plate; • D is the electrostatic deflection; • Θ is the angle between OM & ON (from fig.) (deflecting angle) • VAis the accelerating potential of electron;

13. Transit Time:- The time spent by electron in electric field, given by---- • Deflection Sensitivity :-The deflection caused by one volt of potential difference applied to deflection plates. It is thus, • Deflection Factor:-The reciprocal of deflection sensitivity

14. III) Motion of Electron projected at an angle in uniform electric field : • Thus the motion of electron when projected at an angle in uniform electric field will be very much similar to that of projectile in gravitational field. + _

15. The velocity component in x-direction vx remains constant while vy decreases initially and again increases when the electron reverses its path. Therefore the components are given by, ------------(1) • Using above equations we can obtain coordinates for the electron at any time t --------------(2) --------------(3)

16. From Eqns. (1) & (2) we get ----(4) • Which is of the form and represents the equation of parabola. • Therefore the trajectory of an electron projected into a uniform electric field is a parabola.

17. The various parameter of projected charge particle in uniform electric field can be obtained as follows. • Time of ascent (t): --------(5) -------- (6) 2) Time of flight (T) : --------(7) 3) Height (H): -----(8) 4) Range (R) :

18. MAGNETIC FIELD v θ F B B θ F v • Lorentz force is given by • Force vector will be at right angles to the plane containing velocity vector and field vector. • If v = 0 then FL = 0 , indicating that magnetic force does not act on static electron or electron at rest. For positive particle For negative particle

19. The work done by the magnetic field is • No work is done by the magnetic field in moving the electron from one position to another. • As the force vector is perpendicular to velocity vector, • It means that an electron moves through a magnetic field without acquiring or losing energy.

20. Motion of Electron in Uniform • Magnetic Field B B v = 0 FL = 0 V ║ B FL = 0 1) If θ = 0 or π then FL = 0 , indicating that magnetic force does not act on electron and continue to move along the field lines with initial velocity. 2) If θ = π/2 then FL = evB , indicating that the electron experiences maximum force. electron

21. II] Motion of electron perpendicular to uniform Magnetic field : Xxxxx • Force due to magnetic field is given by F = Bev • Under the influence of this force the electron moves in a circular orbit. • Then the centripetal force required for orbital motion is supplied by the magnetic force.

22. Time period for orbital motion is • Frequency of revolution f and angular frequency ω of an electron are given as • The time period, frequency of revolution and angular frequency of electron are independent of velocity and radius of circular orbit.

23. III] Motion of electron at an angle to uniform Magnetic field : • Vcosθ will not be affected by the magnetic field and hence electron will continue to move with a constant velocity in the z direction. • Vsinθ will give rise to force F = Bevsinθ • which is constantly applied on a particle in a direction perpendicular to that of both the magnetic field and the motion.

24. Hence the resultant path describe by the electron will be helix whose projection on XZ- plane will be a circle having a radius • Pitch of the helix.

25. Magnetostatic Deflection Magnetostatic Deflection F Q R θθ D C θθ A P o L l Where, L= length of screen from centre of magnetic field. l = length over which the transverse magnetic field is acting. D = PQ = Deflection experienced by the electron beam. R = radii of arc AC.

26. From the fig: • PQ = D = Ltanθ • As θ is very small, • The magnetic deflection sensitivity is given by Thus,

27. FE =eE screen + + + + + + + + X X X X X X X X X X X X X X X X X X e- Electron source v e O FL = FE - - - - - - - - - - - - FL = evB Electric and magnetic field in cross field configuration • Uniform electric and magnetic fields are perpendicular to each other and act over the same region.

28. The force due to electric field is –FE = eE • The force due to magnetic field is – FL = evB • Magnitudes of fields E & B are adjusted such that • FE =FL eE = evB

29. screen FE =eE + + + + + + + + v’ < v X X X X X X X X X X X X X X X X X X X X X X X X X X X v dv O - - - - - - - - - - - - v” > v ‘” FL = evB Velocity Selector (Filter) • An electro-optic device which uses cross field configuration for selecting stream of charged particles of single velocity from beam of charged particles having wide range of velocities.

30. THANK YOU