Two Chapter 8

The Mass of the Electron and Proton

• From Thomson's experiment the direction of deflection by magnetic and/or electric fields indicated that the electron was negatively charged
• With just an electric field present, the Thomson's apparatus as illustrated in section One Chapter 8, would deflect particles in the upward direction.
• With just a magnetic field present, the particles could be deflected in the opposite direction (For our discussion, that would be down).
• When both electric and magnetic fields were present, the field strengths could be adjusted so that the effects of each field independently could be cancelled. Therefore, the particles would travel straight through as if neither field was present.
• With just the magnetic field, the path of the particles is circular, therefore,

F_mag = F_centripetal = F_c

or

evB = (mv²)/r

or

e/m = v/(rB) Equation 1

• In these equations, F_mag = magnetic force on the particles, F_c = centripetal force on the particles, e = the charge on the particles, v = the velocity of the particles, B = the magnetic field strength, m = the mass of the particles, and r = the radius of the circular path.
• r can be measured directly.

• Because the particles go straight,

F_mag = F_elec

or

evB = eE

or

v = E/B Equation 3

• In these equations, F_elec = electric force, and E = electric field between the plates in the Thomson apparatus. Therefore,

V = Ed

or

E = V/d Equation 4

• Here we have V (capital) = the electric potential between the plates, and d is the distance between the plates in the Thomson apparatus. Of course Thomson built the apparatus, and so he knows the value of d, and V can be measured with a volt meter.
• Substituting equation 4 into equation 3 and rearranging gives

v = V/(dB) Equation 5

• Substituting Equation 5, and equation 2 into equation 1 gives

e/m = (2Vd)/((x²+d²)B²) Equation 6

• The value of B can be calculated by the physical dimentions of the coil (solinoid), (See Three Chapter 6).
• Since Thomson was able to determine all the values in the right hand side of equation 6, he was therefore able to calculate, the charge to mass ratio for the electron

e/m = -1.76 X 10¹¹ C/kg

• Millikan, a few years after Thomson performed his experiment, determined that the charge on the electron is

e = -1.6 X 10^-19 C

• Therefore,

e/m = -1.76 X 10¹¹ C/kg = (-1.6 X 10^-19 C)/m

or

m_e = 9.11 X 10^-31 kg

• m_e = the mass of the electron
• The mass of the proton can similarly be determined

m_p = 1.67 X 10^-27 kg

• Essentially, Thomson's experiment can be used to find the charge-to-mass ratio for any charged particle. The equation is the same (Equation 6) or

(q/m) = E/(B²r) Equation 7

Application of Cathode Rays

• In the cathode ray tube (CRT)
  • A filament heats the cathode. This causes the emission of electrons (Thermionic emission to be discussed later).
  • Emitted electrons are accelerated towards a cylindrical anode.
  • On the way, the electrons pass through a control grid or electrode (grid of very fine wire).
  • The control grid controls the number of electrons passing through it by the amount of charge on it.
  • Electrons pass through one or more focusing electrodes which concentrate the electrons in a fine beam.
  • The electron beam is deflected by pairs of magnetic coils or charged plates.
  • The electrons fall on a screen at the end of the tube which is covered with a thin coat of phosphors.
  • The phosphors give off light when struck.
  • The color of the light depends upon the type of phosphors used.
• Oscilloscopes - a device used in electronics to make stationary patterns representing electrical signals.
  • Electrons are deflected by two sets of charged plates.
  • The beam is deflected across the screen at a chosen rate.
    • A signal is sent to horizontal deflection plates to accomplish this deflection.
  • The input signal is applied to the second set of plates to cause vertical deflection.
  • Electronic circuitry causes the pattern to repeat the same path as long as the input remains the same.
• Cathode Ray Television (A rare find these days)
  • Inside of the tube a coating of phosphors gives off a bluish-white glow when struck by electrons (black and white TV).
  • The electron beam sweeps across the screen back and forth in 1/30 s.
  • The beam intensity is controled by control electrodes. A more intense beam produces a whiter spot.
  • The potential difference on the control electrode is changed by the signal from the station.
  • For Color television, the tube is coated with three different colors of phosphors arranged in vertical bars.
    • Three electron beams are aimed at the tube and each sweeps the line in 1/30 s.
    • Between the electron gun and the screen is placed a shaddow mask which ensures that light from the red electron beam hits only the red phosphor strip. Similarly for the green and blue guns.
    • The television station must send out information for each of the control grids in each of the three guns as well as information for the sound
• Radar - Radio detection and ranging
  • The electron beam is synchronized with the pulses of microwaves sent out by a rotating radar antenna.
  • The rotating antenna sends out a pulse, and the electron beam is deflected outwards from the center of the screen in a direction corresponding to the direction of the antenna.
  • When a return signal is received, it is sent to the control grid which causes an increase in intensity of the electron beam. This then produces a bright spot on the screen.
  • The distance from the screen center indicates the distance to the object.
  • This provides a 360^o picture of what is in the air around the station.
• X-Rays
  • X-rays are produced by using a type of cathode ray tube (see section five chapter 7).

• It must be pointed out that many of these applications of cathode rays have been replaced now with newer more efficient technologies. Televisions are a good example. Most televisions are now either plasma televisions, LED televisions or LCD televisions which all use much different technologies.
• In spite of the newer technologies, the older technologies illustrate the use of the fundamental principles related to electric charges, magnetic fields, particle beams such and cathode rays, and electromagnetic waves, and form a useful discussion of the principles.

January 19, 2014