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9.4.A - Cathode Rays


By the mid 1800s, physicists were well aware of the force experienced by moving charges in electric and magnetic fields. When the cathode ray tube was invented in 1855, they used their knowledge to investigate a strange new phenonemenon known as cathode rays. After some thirty years of debate about whether cathode rays were particles or waves, Thomson used a cathode ray tube and magnetic and electric fields to deduce that they were actually a stream of negatively charged particles now known as electrons. In this important experiment, he basically discovered the electron and measured the ratio of its mass to charge by balancing the electric and magnetic force on a cathode ray beam. This disovery had many important applications including the development of the cathode ray tube which was used in early televisions and computer screens.

In this unit you will learn:

  • That electric field is defined as force per unit positive charge
  • That charges experience a force when placed in an electric field
  • That electric force is experienced parallel to the field lines
  • That magnetic field is defined as force per unit positive charge
  • That moving charges experience a force when placed in a magnetic field
  • That magnetic force is experienced perpendicular to the field lines
  • About Thomson's experiment to determine charge to mass ratio
  • About the historical development of ideas regarding cathode rays
  • About the observed behaviour of cathode ray tubes and corresponding explanations
  • The reasons for the debate about cathode rays being waves or particles


Magnetic Fields

Charged particles will always experience a force when placed in a magnetic field if they are moving in a direction that is NOT parallel to the field lines. The force will increase in proportion to the velocity, the magnetic field strength and the size of the charge. The force will be a maximum when the charge's velocity vector is perpendicular to the magnetic field lines.

Said mathematically, a positive charge q moving with velocity v through a magnetic field of flux density B will be subjected to a force given by the formula below.

Equation - Force on Moving Charges in a Magnetic Field
F = Bvqsinθ

F

B

v

q

θ

force on the charge

magnetic field strength

velocity of the charge

size of the charge

angle between velocity vector and the field lines

newtons (N)

teslas (T)

metres per second (ms-1)

couombs (C)

degrees (°)

You should use this equation when calculating the magnitude of the force on a charge moving in a magnetic field. Not that if the charge is not moving there will be no force.


The direction of the force is most easily determined using the right hand palm rule for a positive charge and the left hand for a negative charge.

It follows that if a moving charge enters the magnetic field at 90° to the field lines, it will be subject to a force at 90° to the velocity vector. Because sin90° = 1, the formula describing the force on the charge is simplified to F = qvB and the force will be a maximum. When the velocity vector is parallel to the field lines, sin°=0 and the force will be zero.

Click here to watch a video from Physical Science by Derek Owens showing how the direction of force on a charge can be determined.

The path of a positive charge entering a perpendicular magnetic field will be
circular. Note the equivalence of centripetal and magnetic force to determine
the velocity of the charge.

When a charge enters a magnetic field perpendicular to the field lines, the force will change the direction of the velocity vector but only in the two dimensions represented by the plane of the page in the diagram. The velocity vector will still remain perpendicular to the dimension within which the field lines run.

The force is always perpendicular to the tangent of a circle representing the charges motion. Since the force is always directed toward the centre of a circle, this is a type of uniform circular motion. Equating the equations for centripetal force and magnetic force can be a useful way of determining the velocity of the charge.



A short video showing how the force on a charge entering at right angles to magnetic field is always directed
towards the centre of a circle and creates uniform circular motion.

 

Electric Fields

Common electric fields between point charges and charged
plates. Field lines always leave or enter a charge
perpendicular to the surface or the tangent to the surface.
The dotted lines are lines of equipotential or places where
the electrical field strength is constant.

Electric fields are found around charged objects and can be thought of in terms of a 'region of influence'. They are represented by lines with arrows that, by convention, originate at a region of positive charge and are directed towards a region of negative charge.

The electric field is defined as the force experienced by a positive test charge placed in the field of a source charge.

The force on a positive test charge will be directed away from a positive source charge and towards a negative source charge. Lines that are closer together (or more dense) represent greater electric field strength.

Electric field strength is measured in volts per metre (Vm-1) or newtons per coulomb (NC-1).

The electric field surrounding a point charge is a radial electric field.

The electric field between two parallel plates.

When two metal plates are arranged in parallel in proximity with a separation and one plate is carrying a positive charge and the other a negative charge, an electric field is set-up as shown in the diagram on the right. Since the field lines are uniformly spaced, the electric field is constant between the plates.

The charging of the two plates shown in the diagram could be achieved by earthing the negative plate and connecting the positive plate to a charged object such as a Van der Graaf generator (assumed here to be positive). As a charge of +q is established on the positive plate and electrons flow in from earth, because of charging by induction, to create a -q charge on the negative one. The charging of the two plates could also be achieved by connecting the plates to the terminals of a battery or other source of large DC voltage.

Click here to watch a video from Physical Science by Derek Owens about electric fields and electric field strength.

Click here to watch another video from Physical Science by Derek Owens about charged particles in electric fields.

Equations for calculations involving electric field strength and electric force are summarised below.

Equation - Electric Field Strength
E = V/d

E

V

d

electric field strength

potential difference (voltage)

distance between parallel plates

volts per metre (Vm-1)

volts (V)

metres (m)

You should use this equation when calculating the uniform electric field between two parallel charged plates.

 

Equation - Electric Force
F = Eq

E = F/q

F

E

q

force on the charge

electric field strength

size of charge

newtons (N)

newtons per coulomb (NC-1)

coulombs (C)

You should use this equation when calculating the magnitude of the force experienced by a charge placed somewhere in an electric field.

 

Cathode Rays

In 1855 (because his tedious social life failed to satisfy him) the German inventor and glassblower Heinrich Geissler, invented a vacuum pump that could remove enough gas from a glass tube to reduce the pressure to 0.01% of normal air pressure at sea level (101.3 kPa). His friend Julius Plucker (who was also searching for an antidote to the mindless chit-chat thinly veiled as satisfying social intercourse at high-society parties) experimented with the apparatus by passing an electrical current through the gases in the tube at low pressure. Plucker sealed electrodes into a glass tube and then evacuated the tube to very low pressure.

A typical cathode ray tube connectd to a high voltage source
such as an induction coil.

When Plucker applied very high voltage to the electrodes, current flowed through the tube and he noticed that the glass tube itself glowed with a pale green glow, mainly in the vicinity of the anode (positive terminal). He concluded that rays of some form were emanating from the cathode (negative electrode) and that these rays caused the glass to glow. These rays were eventually named cathode rays because they appeared to come from the cathode (negative electrode) of the tube. Plucker also showed that the rays were deflected by an external magnetic field.

When we repeat Plucker's investigations in the laboratory, we find that different patterns of light are observed in the tube as the pressure is gradually reduced as summarised in the table below.

Pressure (kPa)
Observations
Image
5.3
This is the greatest air pressure in this series of photographs. Flickering blue and violet streamers of electrical discharge appear in the tube.
1.3
Striations are just visible.
0.8
The positive striations are very clear.
0.4
The positive column breaks into bands called striations.
0.2
A faint glow of light appears around the cathode. The positive striations are just visible.
0.04
At this low air pressure there is no longer enough gases in the tube to fluoresce. The cathode rays are striking the glass tube behind the anode and the glass is fluorescing.

 


The typical pattern of striations and spaces in a low pressure cathode ray tube.

The diagram on the right shows how the cathode ray tube above would look at 0.4 kPa with the various glows and dark spaces labelled.

The voltage applied between the cathode and anode is a high voltage and is usually supplied by an induction coil.

In 1885, Sir William Crookes was also investigating cathode rays and he also showed that a heated cathode produced the same cathode rays which could cause gases at low pressures to glow and make other substances emit light. There was some debate about whether cathode rays were particles of waves. Some of the experimental evidence at the time conflicted which led the German scientists to deduce that they were electromagnetic waves and the English scientists that they were particles.

The experiments conducted on cathode rays, their results and conclusions are summarised in the tables below.

Experiment
Description
Result
Conclusion
Maltese Cross

An opaque object like a metal cross is placed in the path of cathode rays in a discharge tube.

A clear shadow with sharp boundaries is formed Cathode rays travel in straight lines
Paddle Wheel

A light paddle wheel is placed in the path of cathode rays in a discharge tube.

Cathode rays move a paddle wheel Cathode rays have momentum and therefore mass
Magnetic Field

A magnetic field is applied in the path of cathode rays.

Cathode rays are deflected Cathode rays are particles with a negative charge
Electric Field

An electric field is applied in the path of cathode ray.

Initially: no deflection was detected (Crookes)

1887: deflection of cathode rays towards the positive plate (Thomson)

Cathode rays did not carry charge.

 

Cathode rays were negatively charged.

 

Note that Crookes also believed that cathode rays could be deflected by an electric field but never succeeded in demonstrating this experimentally. It was Thompson in 1897 that showed definitively that cathode rays were particles when he demonstrated deflection in an electric field. When Crooke’s did the experiment, the technology was not sufficiently developed to show deflection, as his tubes could not be evacuated to a low enough pressure. At these higher pressures, electrons were ionising the gas in the tube and the positive and negative ions were forming layers at the sides of the tube and shielding the electrons from the effects of the external electric field.

Some of the properties above suggested to physicists that cathode rays were a wave similar to light.  For instance, they produced energy, they travelled in straight lines, they produced similar chemical reactions to those produced by light and they were not deflected by electric fields.  Yet cathode rays were deflected by a magnetic field as if they were negatively charged particles.  This apparently inconsistent behaviour of cathode rays led to much controversy over whether the rays were a stream of negatively charged particles or a form of EM wave like light.

By the end of the 19th Century, the argument in favour of cathode rays being charged particles had become much stronger.  By then, it had been shown by Eugen Goldstein that the rays could be deflected by electric fields and by Jean Perrin that the charge on the rays was negative.  The final piece of evidence was provided by Thompson in a brilliant experiment conducted in 1897.

 

Thomson's Experiment

Karl Braun invented a cathode ray tube with a fluorescent screen making up one end of the tube in 1897. Shortly after this, Thomson used this technology to perform a series of experiments to determine the true nature of cathode rays. Having established that cathode rays were negatively charged particles, Thomson analysed his data to determine exactly what these particles were. At this point it is important that you understand that no subatomic particles were known to exist.

To investigate the particles making up the cathode ray, Thomson made measurements of the charge to mass ratio of cathode rays. Thomson’s method used both electrostatic and magnetic deflection of the cathode rays to determine the charge to mass ratio for the particles that made up the cathode rays. The apparatus shown in the following diagrams could be set up so that it created a magnetic field that was perpendicular to both the electric field and the trajectory of the cathode rays and effectively cancel these two forces.

Thomson assumed the cathode ray to be made up of particles with a negative charge. He then considered the cathode ray beam to be made up of particles of mass m and charge e, travelling at velocity v. He then considered what happened when the beam passed through an electric field in the region between the charged plates and through a magnetic field.

The method used to calculate the charge to mass ratio of the electron (q/m) was as follows:

Step Equations Diagram

The electrons in a cathode ray beam experience a force perpendicular to the magnetic field lines, so the beam is deflected.

The electrons in the cathode ray beam undergo circular motion due to the magnetic force. This force is equal to F = mv2/r, where m was the mass of the particles and r was effectively the distance of deflection of the cathode ray beam from the centre of the screen at the end of the cathode ray tube.

The magnetic field strength (B) was known and the velocity was determined in the last step below.

Equating these two forces leads to the relationship:

Considering the electric field only, the electrons in a cathode ray beam experience a force parallel to the electric field lines, so the beam is deflected.

To work out the velocity, Thomson created an experiment where a beam of cathode rays simultaneously passed through an electric and magnetic field. He adjusted B so that the beam was undeflected as shown in the diagram on the right, creating a situation where B and E were equal and opposite. Since both E and B were known or calculable quantities, the velocity of the beam could be determined using the equations on the right.

Equating these two forces leads to the relationship:

 

JJ Thomson in his laboratory c1897 with a cathode ray tube.

The two formulas above could not give the charge or the mass of the cathode ray particle that subsequently became known as the electron. All Thomson knew was that the q/m ratio was around 1800 times larger than that for a hydrogen ion. The only conclusions possible were that the electron was carrying a charge that was 1800 times greater than the hydrogen ion (proton) or that the electron was 1800 times less heavy.

Thomson then performed a series of relatively inaccurate experiments to determine the charge on the electron and found it to be approximately the same as a hydrogen ion. This convinced him that the mass of an electron was in all likelihood around 1800 times less massive than the mass of a hydrogen ion.

In 1908, Robert Millikan and his then graduate student Harvey Fletcher did the famous oil-drop experiment to measure the charge of the electron (as well as the electron mass, and Avogadro's number, since their relation to the electron charge was known). It was from this experiment and Thomson's experiment that the mass of an electron could then be determined.

 

Applications of Cathode Rays

Cathode Ray Oscilliscope

The main components of a typical cathode ray tube. The heating
filament (H) provides a source of electrons that are accelerated by
a strong electric field from the cathode (C) to the anode (A). The
cathode and anode also act as collimators tofocus the electrons into
a suitably thin beam.

A cathode ray oscilliscope contains a cathode ray tube as its main component. The important parts of a cathode ray tube include the electron gun, the deflecting plates and the fluorescent screen. In the electron gun the heating filament heats the cathode, releasing electrons by thermionic emission. A number of electrodes are used to control the brightness of the beam, to focus the beam and accelerate the electrons along the tube. Electrons are negatively charged particles and the positively charged anode develops a strong electric field that exerts a force on the electrons, accelerating them along the tube.

Regulating the number of electrons striking the screen controls the brightness of the display. This is achieved using a grid situated between the anode and the cathode that is at a more negative voltage than the cathode. The grid repels electrons, reducing the number reaching the anode and decreasing the number hitting the screen. Increasing the negative voltage at the grid with respect to the cathode will, therefore, decrease the brightness.

The electron gun contains two anodes and the beam is focused by changing the positive voltages on the anodes. Two sets of parallel deflecting plates are charged to produce an electric field that can deflect the beam of electrons separately, up or down or left or right. These fields are used to move the beam so that the electrons can be directed to all points on the fluorescent screen. The glass screen is coated with layers of fluorescent material. It emits light when high-energy electrons strike it.

A typical cathode ray osciiliscope used to produce waveforms
from a varying input voltage.

A cathode ray oscilloscope (CRO) this system to create a waveform on a screen. A CRO uses a cathode ray to display a variety of electrical signals. The horizontal direction is usually provided by a time base (or sweep generator) which allows the voltage (on the vertical axis) to be plotted as a function of time (on the horizontal axis). This enables complex waveforms or very short pulses to be displayed and measured. The voltage input is amplified and the signal directed towards the vertical deflection plates. The horizontal time sweep signal is referred to the horizontal deflection plates provide a voltage that drives the beam across the screen at a constant rate. Both sets of plates work together to produce a waveform on the fluorescent screen.

Televisions

Older style televisions or computer screens work in basically the same way as a cathode ray oscilliscope but with some notable differences. An electron gun still produces a cathode ray beam but in a television the beam is deflected by electromagnets or coils of wire which produce a magnetic force rather than an electrical one. Colour televisions also contain three electron guns which each focus their electron beams on one of three little dots on the back of the screen, one for red, one for green, and one for blue. They chose these colours because together, red, green, and blue create white light, and, in different combinations, can create any colour.

A mask in the back of a
television screen showing
the red, blue and green
phosphors.

Electrons accelerating towards the back of the screem are headed for a phosphor. A phosphor is any material that when hit with radiation (or, in this case, the electron beam) emits visible light. The back of a television screen is coated with phosphors. When the electron beam hits the phosphors, a photon of light is given off of a particular colour corresponding to whatever electron gun had firec the electron beam. Phosphors are usually set into a mask in groups of three: red, green and blue corresponding to each of the three electron guns.

Cutaway rendering of a color CRT:
(1) Three electron guns (for red, green, and
blue phosphor dots), (2) Electron beams
(3) Focusing electromagnet coils,
(4) Deflection coils, (5) Anode connection,
(6) Mask for separating beams for red, green
and blue part of displayed image,
(7) Phosphor layer with red, green and blue
zones and (8) Close-up of the phosphor-coated
inner side of the screen.

Standard televisions use an interlacing technique when painting the screen. In this technique, the screen is painted 60 times per second but only half of the lines are painted per frame. The beam paints every other line (odd numbered lines) as it moves down the screen. Then, the next time it moves down the screen it paints the even-numbered lines, alternating back and forth between even-numbered and odd-numbered lines on each pass. The entire screen, in two passes, is painted 30 times every second. The alternative to interlacing is called progressive scanning, which paints every line on the screen 60 times per second. Most computer monitors use progressive scanning because it significantly reduces flicker. Because the electron beam is painting all 525 lines 30 times per second, it paints a total of 15,750 lines per second. Some people can actually hear this frequency as a very high-pitched sound emitted when the television is on).

When a television station wants to broadcast a signal to your television, or when your DVD wants to display the movie on a disc on your television, the signal needs to mesh with the electronics controlling the beam so that the television can accurately paint the picture that the television station or DVD sends. The television station or VCR therefore sends a well-known signal to the television that contains three different parts:

  • Intensity information for the beam as it paints each line
  • Horizontal retrace signals to tell the TV when to move the beam back at the end of each line
  • Vertical retrace signals 60 times per second to move the beam from bottom-right to top-left

There are two sets of electromagnets at the back of the cathode ray tube that control the deflection of the electron beams and ensure that it is sweeping the screen at the frequencies specified in the horizontal and vertical retrace signals.