In a parallel plate capacitor the anode is made 350 V positive with respect to the cathode
and it is 6 mm from it. An electron is emitted from the cathode at a velocity of 3× 106 m/s
straight in the direction of the anode. Calculate the velocity and the time of travel of the
electron when (i) the electron is midway between the anode and cathode, (ii) the electron
reaches the anode. (Mass of the electron is 9.1 × 10−31 kg)
Answers
Thermionic emission of electrons occurs when free electrons are
emitted from the surface of a heated cathode.
● The work done on an electron which is accelerated through a
potential difference, V, is equal to eV.
● The specific charge of a particle is defined as the charge per unit
mass. It has units of C kg-1
.
● An object falling due to gravity will reach a terminal speed. The
speed will depend on the drag force experienced by the object. Drag
increases with the size of the object and the speed with which it is
falling.
● A charged particle in a uniform electric field will experience a force,
FE, which depends on the magnitude of the field, E.
FE = EQ
where E is the field strength of the electric field, measured in V m-1
(or N C-1
), and Q is the charge of the particle in C.
● A charged particle travelling in a direction perpendicular to a
magnetic field will experience a force, FB which depends on the
magnitude of the field and the speed at which the particle is moving.
The direction of the force is determined by Fleming’s left hand rule.
FE = BQv
where B is the magnetic flux density in T, Q is the charge of the
particle in C and v is the velocity of the particle in ms-1. The particle
will follow a circular path with radius r.
● A particle which experiences a force, F, perpendicular to its direction
of motion will follow a circular path.
F = mv
r
2
where m is the mass of the particle in kg, v is the velocity of the
particle in m s–1, and r is the radius of the path in m.
Wave-particle duality
● When light is reflected from a boundary the angle of incidence is
equal to the angle of reflection.
● Light is refracted when it crosses the boundary between two
materials with different optical density; the light changes speed and
direction.
● Waves can undergo constructive or destructive interference.
● In Young’s double slit experiment, a single light source may be used
with double slits to produce an interference pattern. The fringe
spacing is given by
W = lD
s
where λ is the wavelength of the light, D is the distance between the
double slits and the screen, and s is theTEsT yoursELF on PrIor KnoWLEDgE 1 Calculate the energy of an electron when it moves through a potential
difference of 6 V in electron volts, and in joules.
2 Use the data in Table 16.1 to calculate the specific charge of the
proton.
Mass/kg charge/c
Proton 1.673
¥ 10
-27
+1.60
¥ 10
-19
Table 16.1
3 An electron is accelerated in a uniform electric field between two
electrodes which are 4.0 mm apart. The p.d. between the electrodes
is 20 V. Calculate the force acting on the electron.
4 A particle is travelling with a speed of 1
¥ 10
6
m s
-
1
perpendicular to a
magnetic field with magnetic flux density of 0.13 T. The particle has a
charge of 3.62
¥ 10
-
6
C; calculate the force acting on the particle.
5 A student shines monochromatic light of wavelength 580 nm through
two slits 0.25 mm apart. The screen is 2.3 m away.
a) What is the frequency of the light?
b) What is the separation of the interference fringes observed on the
screen?
6 Explain why a laser is often used to carry out Young’s double slit
experiment.
7 Calculate the wavelength of an electron moving at 0.1% of the speed
of light. The mass of an electron is 9.1
¥ 10
-31 kg.
22
Isaac Newton, in a letter to Robert Hooke, wrote: ‘If I have seen further, it is by
standing on the shoulders of Giants’. Physics is often thought of as continually
developing so that each new discovery or theory builds on those that
happened before it. Each new generation of physicists stand on the shoulders
of those who have gone before. Newton was making the point that if it had
not been for the work of astronomers such as Copernicus, Brahe, Galileo and
Kepler, he would not have discovered the Universal Theory of Gravitation.
However, there are points in the history of Physics where there is a change
in our understanding of the world, where there is a theory which is very