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BE-II SEMESTER ADVANCED PHYSICS. UNIT-II ELECTRON BALLISTICS DEPARTMENT OF APPLIED PHYSICS. SYLLABUS. Introduction, Motion of charged particle in parallel & perpendicular electric Field. Motion of charged particle Inclined electric Field, electrostatic deflection.
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BE-II SEMESTER ADVANCED PHYSICS UNIT-II ELECTRON BALLISTICS DEPARTMENT OF APPLIED PHYSICS
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
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
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
- 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
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
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,
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 .
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.
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.
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
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;
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
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. + _
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)
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.
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) :
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
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.
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
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.
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.
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.
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.
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.
From the fig: • PQ = D = Ltanθ • As θ is very small, • The magnetic deflection sensitivity is given by Thus,
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.
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
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.