Mathematically we can write,Į is the potential difference between the two plates,

By the conservation of energy, we have loss in potential energy when the electron moves from cathode to accelerating anode should be equal to gain in kinetic energy of electron. Now let us derive an expression for deflection of this beam. The beam deflects by angle A, due presence of electric field and deflection is in the positive direction of y axis as shown in the figure. Now let us consider a beam of electron coming along the x-axis as shown in the figure. After deflection plates we have screen through which we can measure net deflection of the electron beam. The field produced by these plates is in the direction of positive y axis and there is no force along the x-axis. These plates are also called deflection plates. In the above system we have two plates A and B which are at potential +E and 0 respectively. In order to find out the expression for the deflection, let us consider a system as shown below: Therefore this system is also called focusing system. We can from the above equation see that there is bending of the electron beam after passing through the equipotential surface. Now we have relation as sin(A)/sin(B)=V 2 / V 1. It means that the tangential velocities will remain same, so by equating the tangential components we have V 1sin (A) = V 2sin(B), where V 1 is the initial velocity of the electrons, V 2 is the velocity after passing through the surface. The normal component of velocity of the beam will increase as force is acting in s direction normal to the surface.

When a beam of electron is incident at angle A to the normal then it deflects by angle B after passing through the surface S as shown in the figure given below. The potential on the right side of the surface is +E while the potential on the left side of the surface –E. Let us consider the curved equipotential surface S as shown below. Now here we are interested in calculating the deflection angle of electron beam when it passes through this curved equipotential surface. The equipotential surfaces are marked by the dotted lines which are curved in shape. The resultant direction of electric field and the equipotential surfaces are also shown in the figure. Here we have two concentric cylinders with a potential difference applied between them as shown in the figure. The deflection angle can be easily varied by changing the potential of the plates. As the beam of electron passes through this plate system, it deflects in the opposite direction of electric field. The equipotential surfaces are also shown in the diagram which is perpendicular to the direction of electric field. The direction of electric field is from A plate to plate B at right angle to the surfaces of the plate. The plate A is at potential +E while the plate B is at potential –E. In this case we are having two plates A and B as shown in the figure.

Now we will this force to defect the beam of electrons coming out of electron gun. We know that the force on an electron is given by – qE, where q is the charge on electron (q = 1.6 × 10 -19 C), E is the electric field intensity and negative sign shows that the direction of force is in opposite direction to that of electric field. Here we will discuss electrostatic focusing method in detail. Now there are two methods of focusing the electron beam and are written below: The focusing anode is connected to adjustable voltage 500 volts. Now after this the function of the focusing anode is to focus the beam of the electrons so produced. The pre-accelerating and accelerating anodes are connected to a common positive potential of 1500 volts. After passing through the control grid these electrons are accelerated with the help of pre-accelerating and accelerating anodes. As the name suggests the control grid with its negative bias, controls the number of electrons or indirectly we can say the intensity of emitted electrons from cathode. The electrons after this passes through a small hole called control grid which is made up of nickel. In order to obtain the high emission of electrons the layer of barium oxide (which is deposited on the end of cathode) is indirectly heated at moderate temperature. It consists of six parts namely heater, a cathode, a grid, a pre-accelerating anode, a focusing anode and an accelerating anode. It is the source of accelerated, energized and focused beam of electrons. We’ll now discuss these 5 components in detail: You will need all 5 of these components to build your own DIY oscilloscope.

Cathode ray experiment diagram