HSC Physics Module 9.4 Summary

HSC Physics Module 9.4 Summary

Increased understanding of cathode rays led to the development of television

Identify that moving charged particles in a magnetic field experience a force

Recall that a current carrying conductor experiences a force in a magnetic field, and that current is the movement of charges
The moving charges in the conductor in the magnetic field cause the conductor to experience a force
Generally, any charge or collection of charges moving relative to a magnetic field will experience a force

Identify that charged plates produce an electric field

Recall that an electric field is a region where charged objects will experience a force, and that a point charge or collection of charges will produce an electric field
When two charged plates are brought together, they will exert a force on each other, thus an electric field exists between the plates
See below for diagrams of the electric field between two oppositely-charged plates.

Describe quantitatively the force acting on a charge moving through a magnetic field

As mentioned above, a charge moving through a magnetic field will experience a force
The magnitude of the force a moving charge experiences in a magnetic field is given by:

where:

F = Force [N]
q = Charge [C]Note: 1 coulomb = 6.24x1018 elementary (electron) charges
v = velocity [ms-1]
B = magnetic field strength [Tesla]
Θ = angle between the velocity and the direction of the magnetic field lines

The term sinΘ is included because only the component of the charge’s velocity perpendicular to the magnetic field is subject to a force

The direction of the force can either be given by either the right-hand-palm rule or general right-hand rule
For the right-hand-palm rule, point the thumb in the component of velocity of a POSITIVE charge perpendicular to the magnetic field (opposite direction for a negative charge), and the fingers in the direction of the magnetic field. The palm will point in the direction of the force.
For the right-hand rule, point the fingers in the component of velocity of a positive charge perpendicular to the magnetic field, and curl fingers in the direction of the magnetic field. The thumb will point in the direction of the force.

Discuss qualitatively the electric field strength due to a point charge, positive and negative charges and oppositely charged parallel plates

The strength and direction of electric fields can be represented by flux lines.
The strength of an electric field is the relative magnitude of force a charged particle would experience in the field
The direction of an electric field is defined as the direction a positive charge would experience a force in the field
Thus a negative charge would move in the opposite direction to direction of the flux lines if it were placed in an electric field
A number of rules apply to the interpretation of electric field diagrams using flux lines:
Flux lines begin on positive charges and end on negative charges
Flux lines never cross
Flux lines enter and exit at right angles only
Flux lines that are close together represent strong fields
Flux lines that are well-separated represent weak fields
A negative charge placed in the field will experience a force in the direction opposite to the arrow of the flux lines

FIELDS OF POINT CHARGES

The field strength of a point charge obeys the inverse square law, thus the field strength decreases proportionally to the inverse square of the distance to the charge
Thus we can consider the electric field around a point charge to be radial
Point charges with a stronger charge produce stronger electric fields, which are represented by closer field lines in electric field diagrams
When multiple charges are placed closed together, the resultant field is the superposition of the fields of each charge
The diagram below shows the electric fields of point charges of equal/opposite charge

The diagram below shows the superposition of electric fields of charges of different magnitudes of charge

FIELDS OF OPPOSITELY-CHARGED PARALLEL PLATES

Oppositely-charged parallel plates, also known as parallel-plate capacitors, produce uniform electric fields
If the area of the parallel plates is significantly greater than the distance between the plates, the resulting electric field will be uniform, except at the edges where it slightly bulges
When drawing the electric field between two parallel plates, remember the following:
The flux lines must be evenly spaced
The flux lines should bulge at the edge of the plates
The flux lines should go from the positively-charged plate to the negatively-charged plate
Below is a diagram of the field between two oppositely-charged parallel plates

Describe quantitatively the electric field due to oppositely charged parallel plates

Recall that the magnitude of an electric field is equal to the force per unit charge at a point in the field, given by

Where

E = electric field strength [NC-1]
q = charge [C]
F = force on the charged object [N]

Recall that voltage is the change in potential energy or work done on charge per unit charge, given by

But work also equals force multiplied by distance. Therefore…

Equating the two expressions for work, we get

Dividing be q and rearranging we get

Where

E = electric field strength in between the plates [Vm-1]
V = potential difference between the plates [V]
d = distance between the plates [m]

Thus the electric field between two oppositely-charged parallel plates can be calculated by considering the potential difference and distance between the two plates
When using the above formula, quote the units as Vm-1 rather than NC-1. Whilst both units are equal, quote the units for field strength according to the equation used.
Thus we can see from the above formula that the electric field strength is…
Proportional to the potential difference between the plates
Inversely proportional to the distance between the plates
Equal at all points between the plates
Perpendicular to the plates everywhere in the region between the plates

Solve problems and analyse information using:

ALWAYS specify the direction of any vectors, including force, electric field, and magnetic field
Ensure all calculations include dimensions and are dimensionally correct

IMPORTANT NOTES

Use your right-hand when working out the direction
Crosses mean that the field is INTO the page, points mean OUT of page
When calculating the force an electron experiences in either a magnetic field, reverse the direction of velocity when working out the direction of force
When calculating the force an electron experiences in an electric field, ensure the force is in the direction opposite to a magnetic field

Explain why the apparent inconsistent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves

Cathode rays were observed during the 19th century in vacuum tubes with two electrodes inside and a voltage applied. Their presence was detected by the glowing glass opposite of the cathode (negative electrode).
Scientists determined that the glow was due to a ray emitted from the cathode (hence their name cathode rays), but their properties were inconsistent with both particle and wave motions.
The conflicting observations led physicists to become divided on whether cathode rays were particles or electromagnetic waves
For example, Crookes demonstrated that cathode rays were deflected by magnetic fields (which supports the particle model), but Hertz showed that cathode rays weren’t deflected by electric fields (which supports the wave model)
Hertz’s experiment was later shown to be flawed however, as Thomson demonstrated the deflection of cathode rays due to an electric field by using a more complete vacuum than Hertz. At higher gas pressures, the cathode rays ionised the gas, which were attracted to the oppositely charged plates, and neutralised the charge on the plates, thus the rays weren’t deflected in Hertz’s experiment.

The following observations supported the wave model:
Cathode rays travelled in straight lines
If an opaque object (such as a Maltese cross) was placed in their path, a shadow of that object appeared
They could pass through thin metal foils without damaging them
The following observations supported the particle model:
The rays left the cathode at right angles to the surface
They were deflected by magnetic fields
Small paddlewheels turned when placed in the path of the rays, showing they had momentum and thus mass
They travelled considerably slower than light.
The apparent inconsistencies of the behaviour of cathode rays were due to the inadequacies of experimental design and the current state of knowledge about the nature of atoms.
The atom was later shown to be predominately empty space, so small electrons could pass through metal foils without causing damage
Thomson showed that the rays were deflected towards the positively charged plate, thus demonstrating that they were negatively charged particles
Further experiments showed that cathode rays were a stream of electrons
The resolution of the inconsistencies of the behaviour of cathode rays is an example of the scientific method, i.e. observations from experiments are interpreted and a hypothesis developed to explain what is thought to be happening. Opposing models are then resolved through improved experimentation, allowing us to gain a greater understanding of the nature of cathode rays.

Explain that cathode ray tubes allowed the manipulation of a stream of charged particles

A cathode ray tube is a highly-evacuated, sealed glass tube containing two electrodes.
The negatively-charged electrode is called the cathode, whilst the positively-charged electrode is called the anode
Remember that cations (positive ions) are attracted to the cathode, and anions (negative ions) are attracted to the anode

Applying a high voltage across the tube causes cathode rays to be produced, which are streams of negatively-charged particles (electrons) to flow from the cathode to the anode, with little obstruction from collisions with remaining gas particles
As cathode rays are negatively-charged, they can be deflected by applying an external electric or magnetic field
In addition, placing solid or otherwise objects in the path modifies the path of the beams
For example…
Applying an external electric field deflects cathode rays to the positive plate, demonstrating that they are negatively charged (parabolic deflection)
Applying an external magnetic field deflects the cathode rays perpendicularly to the magnetic field (circular deflection)
Placing solid objects in the cathode ray tube inhibits the movements of cathode rays
A Maltese cross produces a shadow
A paddlewheel rotates when placed in between the anode and cathode

Outline Thomson’s experiment to measure the charge/mass ratio of an electron

Many of Thomson’s experiments centred on his study of cathode rays, such as his demonstration of the deflection of cathode rays due to an electric field
Thomson was also able to determine the charge to mass ratio of an electron through the analysis of cathode rays
His experimental set-up is shown below:

The glass tube is sealed and at reduced pressure
The cathode rays are emitted from the cathode (negatively-charged electrode)
The anodes consist of charged plates with thin slits => they act as anode collimators, as the cathode ray accelerates towards the plates, passes through the slit, and enters the main tube as fine and well-defined beam
The charged plates produce an electric field (in exams, mark which one is positive, which is negative, and the direction of the field)
The coils act as electromagnets, and produce a magnetic field
The fluorescent screen allows the cathode rays to be detected

His experiment consisted of two steps:
He first varied the magnetic and electric fields until their opposing forces cancelled, leaving the cathode ray undeflected. By equating the magnetic and electric force equations, Thomson was able to determine the velocity of the cathode-ray particles.

He then applied the same strength magnetic field (alone), and determined the radius of the circle path travelled by the charged particles in the magnetic field

As v had already been calculated, and r and B can be measured (r by careful observation), Thomson was able to calculate the charge-to-mass ratio of the particles in the cathode ray
His experiment demonstrated that cathode rays were particles, because if the cathode ray has a charge-to-mass ratio, the cathode-ray particles must have a measurable mass
He calculated that all cathode-ray particles (electrons) had a charge-to-mass ratio of 1.76x1011Ckg-1, regardless of the cathode material, gases, or other conditions
This indicated that the cathode-ray particles (electrons) were common to all materials, which was one piece of evidence indicating that atoms were made of subatomic particles
The calculated charge-to-mass ratio was over a thousand times higher than that of a hydrogen ion (H+), suggesting that the particles were either very light or very highly charged.
Such results contributed to the development of Thomson’s plum-pudding model of the atom

Outline the role of:

electrodes in the electron gun
the deflection plates or coils
fluorescent screen

in the cathode ray tube of conventional TV displays and oscilloscopes

Below is a diagram of the cathode ray tube used in oscilloscopes, which is similar to that used in TV displays with a few differences (see below)

The three primary components of the cathode ray tube used are the electron gun, the deflection plates or coils, and the fluorescent screen.

ELECTRON GUN

The electron gun consists of the cathode, anode collimator, and heater
The cathode emits the cathode rays, which are accelerated towards to the multiple anodes, and then travel into the deflection part of the tube as a fine, well-defined beam
An electrode grid in between the cathode and electrode is used to control the number of electrons reaching the anode, as the grid can be made more positive or negative. This controls the brightness of the display
The heater heats up the cathode, which releases many free electrons that can be easily accelerated towards the cathode => this is called thermionic emission

DEFLECTION PLATES/COILS

The deflection plates or coils produce a unidirectional electric or magnetic field respectively to deflect electrons vertically or horizontally to produce a useful display on the screen
Oscilloscopes use plates to produce an electric field, whilst televisions use coils to produce a magnetic field
There are two sets of parallel plates/coils, each set perpendicularly to each other, so that they can deflect the beam both in the vertical and horizontal direction on the screen according to the voltage applied to the plates/coils
Thus the deflection plates/coils allow the cathode ray to be deflected to any position on the screen

FLUORESCENT SCREEN

The fluorescent screen is coated with layers of fluorescent material, which emits light when high energy electrons strike it
This allows the position of the beam to be seen where it strikes the screen, and allows a useful image to be formed.

Application to the oscilloscope

The CRO (Cathode-Ray Oscilloscope) is a diagnostic tool that allows voltage to be plotted against time
The horizontally-deflecting plates (X-plates) supply a time-based voltage, so the beam sweeps horizontally across the screen in time intervals that can be controlled as desired
The vertically-deflecting plates (Y-plates) are connected to the input voltage (which is amplified as necessary), so their deflection allows the voltage of the input to be measured against time

Application to TV displays

A colour TV display contains three electron guns, each corresponding to the different colours of red, blue and green
The image sent by the signal to the TV is reconstituted on the screen by an additive process involving three coloured phosphors corresponding to red, blue and green.
A shadow mask is used on the screen to ensure the beam from each colour gun only hits the corresponding spot on in each pixel, thus forming the correct image
The TV display use deflection coils (which produce magnetic fields) to deflect the beam
The horizontally- and vertically-deflecting coils are connected to a time-based voltage that scans each line of pixels on the display 50 times a second
The phosphors glow for a short time, so no flickering is observable to the retina
The colour of each pixel is controlled by the intensity of the beam striking its corresponding phosphor, thus an image is formed

Perform an investigation and gather first-hand information to observe the occurrence of different striation patterns for different pressures in discharge tubes

METHOD

An induction coil was connected to a power supply to supply the high voltages required. Discharge tubes of different pressures were connected to the induction coil, one at a time, and the striation patterns that formed were observed and recorded

SAFETY:

Take care when handling the discharge tubes, because the low pressures can cause them to easily IMPLODE (not explode)
The sparks produced emit X-rays, which are potentially dangerous for prolonged exposure. Stand at least 2m away from the coil whilst it is turned on (consider the inverse square law), and only turn the coil on for short periods of time (no more than 5 seconds) for observation
The sparks also produce ozone, which can aggravate respiratory problems => conduct the experiment in a well-ventilated area, and again only turn the induction coil on for short periods of time

RESULTS