Electrostatic Deflection in Cathode Ray Oscilloscope

When an electron beam passes through an electric field a deflection may occur in the beam depending upon the relative direction of the field and the beam. The electrostatic deflection in cathode ray oscilloscope occurs on the basis of this phenomenon.

electrostatic deflection

Upward Electrostatic Deflection of Electron Beam

Suppose ‘m’ is the mass of one electron coming out from the electron gun. The velocity at which this electron comes out from the gun is ‘vx’.

‘Va’ is the accelerating voltage. That means the voltage difference between the cathode and anode of the cathode ray tube (CRT). Again we consider ‘e’ is the charge of one electron.

The kinetic energy obtained by the electron is-

kinetic energy obtained by electron

Since, the charge of the electron is ‘e’ and it crosses the potential difference ‘Va’, we can write,

potential difference

This electron will pass through the fields of horizontal plates and vertical plates. Obviously these two fields are perpendicular to the motion of the electric. Therefore these electric fields can not affect the velocity (vx) of the electron.

So, when the electron entries in the field due to vertical plates (y plates) it will have the same velocity ‘vx’.

Suppose the vertical distance between the y plates is ‘d’.

‘ld’ is the length of each y plate.

‘L’ is the perpendicular distance from the display screen to the meet point of the electric field of y plates.

‘Vd’ is the voltage or potential difference between the y plates.

Therefore the electric field intensity between y plates is-

electric field intensity

Again the force acting on a charged particle in an electric field is the product of the field intensity and charge of the particle.

Therefore the force acting on the electron in between the y plates is-

force acting on the electron between the y plates

Suppose ‘ay’ is the acceleration of the electron due to this force in the vertical direction.

Therefore we can write,

force on the electron


acceleration of electron

Now, the time taken by the electron to cross the y plate is-

time taken by electron to cross the y plate

Therefore the velocity of the electron along the vertical direction is-

velocity of the electron along the vertical direction

This is the vertical velocity of the electron with which the electron leaves the y plates. Therefore we can consider the average velocity in y direction is-

average velocity in y direction


Hence, the vertical deflection at the end of the y plates of the electron is-

vertical deflection of y plate

After leaving the y plates the electron will not undergo through any other electric field. Hence, it will not deflect further. So, it follows a straight line to strike on the phosphor coated display screen.

Hence, from the principle of trigonometry,

electron leaving from y plates

Where ‘D’ is the deflection of the electron from the origin on the display screen.

deflection of electron from the display screen

Again, we have already derived,

deflection of the electron

So, the deflection of the electron or in other words of the electron beam is directly proportional to the voltage (Vd) applied across the y plate.

relation between electron beam and voltage

Sensitivity of CRT

Deflection per volt is the sensitivity of cathode ray tube.


sensitivity of the CRT

Deflection Factor of CRT

This is reciprocal of the sensitivity,

deflection factor of CRT

It signifies the vertical scale of the display screen that means volt per unit length.

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