Electrostatic deflection and sensitivity:-

In a device like CRT,number of electrons are projected by the gun,in form of an electron beam towards the screen.But due to variations in energy,the electrons diverge and cannot produce a dominant spot on the screen.Thus,electrostatic focusing is used.

• It consists of 2 parallel plates called deflecting plates at a distance of 'd' from each other.
• The parallel are subjected to a potential difference of V d,due to which an electric field E exists between the two plates.
• The electrons are emitted by hot cathode k,which are accelerated towards the anode by the potential V a.
• The electrons which are not collected by the anode pass through the small hole at the anode.
• The electrons are focused with the help of deflecting plates on the screen coated with fluorescent material,which are visible to the naked eye.
• This is called electrostatic deflection of the electrons.
• The electrons are emitted by cathode and emerge from anode hole velocity determined by voltage V a,given by V ox =square root of (2eV a/m) .
• The electric field is along Y-axis and is given by E y=V d/d.
• This is similar to motion of an electron in 2-D and the electron moves in parabolic path,and is given by y=[a y/2 V ox 2]*x 2 where a y=E y e /m= e V d/d*m here (q=e)
• Once an electron leaves the region of field,it moves in straight line path till it reaches the screen.
• Slope of the straight line path tan(theta)=dy/dx at x=l =a y*l/V ox 2 ,where l is length of the plates.
• In a line slopes are equal so,(y-l/2)/(x-l)=a y l/V ox 2,thus y=a y l(x-l/2)/V ox 2.
• Thus when y=0,x=l/2 it indicates when the straight line is extended backwards it will intersect the tube axes at point o',i.e the centre of parallel plates.
• The point o' is called virtual cathode .
• Thus y=D,x=(l/2)+L where L=distance from o' to screen,D is the deflection.
• D=l*L*V d/2d V a,thus the electrostatic deflection is directly proportional to V d.
• Electrostatic sensitivity S=D/V d=Ll/2d V a.

Two dimensional motion of an electron:-

Assumptions made are:-

1. The movement of the charged particle is in vacuum so that no collisions of an electron with gas atoms occur.
2. The mass of the charged particle i.e electron is very small and hence gravitational force is neglected,compared to forces due to existing electric fields.
3. The charge density is very low,so that mutual repulsive forces between similar charges is neglected.
4. The distance 'd' is small compared to length of the plates to maintain uniform electric field.

In case of 2-D,the 2 parallel plates are considered in X-Z direction and the intial velocity of the electron is vox is in +ve X-direction.Thus,the electric field(E)is in -ve Y-direction.Since no force is acting along z-direction,acceleration is zero.But as the electric field is in -ve Y-direction,no force acts along x-direction,the electron moves with constant acceleration in +ve x-direction.But as the electric field is also constant ,constant acceleration exists along Y-direction.

• Therefore,the motion of electron is given by a y=v y/t , thus on integration we get y=a y t*t/2
• Also v x =v ox,on integration we get x=v ox*t ,t=x/v ox.
• On substitution we get,y=(a y /2* (v ox) 2)x 2,which represents a parabola.

Motion in a magnetic field:-

Consider a rectangular area ABCD,which represents the cross-section of uniform magnetic field and the direction of magnetic flux is into the paper.Consider a electron is entering into the magnetic field at right angles to the direction of the magnetic field.

• If initially electron is at rest ,then it continues to remain in rest,as no force acts on velocity component perpendicular to magnetic field,which is zero and responsible for the force.
• As the electron is moving,and magnetic field is perpendicular,a force acts on the electron in downward direction,thus the electron will change its direction.
• At every instant,the force acting on the electron is perpendicular to the magnetic field,hence no work is done on the electron and its kinetic energy remains unchanged,as mass of the electron and velocity are constant,the force is also constant
• Hence the path of the electron is circular in uniform magnetic field.

Radius of the circular path:-Let a particle moving in a circle of radius R ,constant speed(v),has a accleration directed towards the centre ,known as centripetal force and given by F=m v 2 /R.

Key point:Force acting on a electron in uniform magnetic field is f m=Bev Newtons if (q=e).

Thus on equating we get,R=mv/Be.

Angular velocity (w= omega):-From circular motion we know that v=Rw,on substituting R we get, w=Be/m radians.

Time period of revoultion(T):-The time required by an electron to complete one revolution is called time period of revolution T.Since T=2(pi)/w=2(pi)m/Be sec

ELECTRON DYNAMICS AND CRO

Intoduction:-

Charged particles:-The electronic devices operate through the motion of the charged particles,usually electrons under electric and magnetic field.The study of trajectories of projectiles usually electrons under the influence of electric and magnetic fields is called as electron ballistics or electron dynamics.

The charge of an electron is 1.6*10^-19 C (where Couloumb (C) is the unit of charge).

Mass of an electron:-The electron poesses a definite mass.A Direct measurment of teh mass of electron cannot be done.The e/m ratio i.e charge/mass ratio is determined by conducting number of experiments as 1.759*10^11C /kg.By knowing e/m value mass of an electron is determined as 9.107*10^-31 kg.

Key point:The radius of an electron is approximately equal to 10^-15 m and that of an atom is 10^-10 m.

Electric field intensity(E):-It is defined as the force on a unit positive charge at any point in an electric field.It's formula is E=V/d volt/metre,where V=Potential in volts,d=distance in metres.

Force on a charged particle in an constant electric field:-

• The force acting on a charge 'q' in an electric field intensity (E) is given by F=Eq.
• But in general to calculate the path of charged particle in an electric field ,the force is related in terms of mass and acceleration of the particle,according to newton's second law we have F=ma=m*dv/dt where (a=dv/dt).
• Thus on equating we get,Eq=ma,therefore a=Eq/m.
• If the electric field is constant and towards the -ve X-direction and the movement of electron is in +ve X-direction,and the electric field components along Y and Z direction are zero,then the above equation changes as a(x)=Eq/m=constant.
• On integrating we get the velocity of the electron in X-direction,v(x)=Eq/m+v(ox) where v(ox) is the intial velocity of electron.
• On further integration we get,the displacement of the particle as x=a(x)t*t/2+v(ox)t+x(o).
• Here x(o) is the intial positon of the electron.
• However,when E is a time varying function ,the above equations are not applicable ,then the equation a(x)=Eq/m,should be integrated where E is time varying and a(x)=dv(x)/dt ,v(x)=dx/dt.