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.