Physical
Electronics
Department of Electrical and Electronics
Engineering
Faculty of Engineering and Technology
University of Ilorin
ELE 323 – Lecture 2
Electrical Field
Intensity for Sheet of
Charge
Suppose an infinite nonconducting plane of charge
place at z=0 has a uniform
charge density . The electric field
above and below the plate is
sketch in Figure 1
Figure 1
Electrical Field
Intensity for Parallel
Plate Capacitor
The device consists of a plate of positive
charge with the negative plate placed above it.
The result is an electric field with double the
magnitude in between the two plates is
illustrated in Figure to the side
Figure 2
Electrical Field
Intensity and Newton
Force
𝐹 = 𝑞. 𝐸
In general:
Note that for electron =
if a charged particle (with charge = 𝑞
Coulombs) move through electric
field (with intensity = 𝐸 volt/m) the
electrostatic force (𝐹 in Newton's)
acting upon this particle is equal to :
q = −𝑒.
F = −𝑒. 𝐸
That’s mean direction of acting force
on negative charge is opposite
direction to direction of electrical field.
Newton’s second law
dynamics
Newton second law determines the
motion of a particle, of mass m,
moving with velocity v and
acceleration a is given by :
𝑑𝑣
F=𝑚
= 𝑚. 𝑎
𝑑𝑡
Combining it with the
former equations:
F = 𝑞. 𝐸
𝑞. 𝐸 = 𝑚. 𝑎
𝑞. 𝐸
𝑎=
𝑚
Velocity:
Velocity and position
of a charged particle
Deducing velocity and position of
the charged particle:
𝑞. 𝐸
𝑎=
𝑚
𝑑𝑣 𝑞. 𝐸
=
𝑑𝑡
𝑚
𝑑𝑣
𝑞.𝐸
Change in velocity: =
𝑑𝑡 ≡ 𝑎. 𝑑𝑡
𝑑𝑡
𝑚
𝑑𝑥
𝑞.𝐸
Change in position: =
𝑑𝑡 ≡ 𝑣. 𝑑𝑡
𝑑𝑡
𝑚
Potential Energy and
Potential
The potential energy ( P.E) is
defined as the work done to
move charge (𝑞) against the
electric field (𝐸) between point
𝑥1 and 𝑥 2 :
Assuming the difference between
the 𝑥1 and 𝑥 2 is L
Such that the change is ∆𝐿
By definition, the electrostatic
potential energy of one point
charge q (𝑥2 ) at position difference
d in the presence of an electric
field EQ of another point charge Q
is the negative of the work done by
to bring q from the reference
position (𝑥1 )
More explanation:
Electrostatic potential
energy of point charge
q in the electric field
of another charge Q
Potential (V) between point 𝑥1 and
𝑥2 is define as the work done to
move positive unit charge (𝑞 = 1)
against the electric field (𝐸)
𝑉 = −𝐸. 𝐿
𝑉 = −𝐸. (𝑥2 − 𝑥1 )
−(𝑉2 − 𝑉1 )
𝐸=
(𝑥2 − 𝑥1 )
𝐸=
−𝑑𝑉
𝑑𝑥
The minus sign shows that the electric field is direction
from the region of higher potential to region of lower
potential.
Concluding on:
Electrostatic potential
energy of point charge
q in the electric field
of another charge Q
If the potential between point 𝑥1 and 𝑥2 was on
straight line with distance 𝐿:
𝐸 =
𝑉2 − 𝑉1
∆𝑉
=
𝐿
𝐿
So we can see that 𝐸 = 𝑞𝑉, and for electrons 𝐸 = −𝑒𝑉
Electron Volt Unit of
Energy
The unit of energy is Joule (J), but
in electronic system it's too
large. The unit of work or energy
usually used called electron volt
(eV) which define as:
1.6 × 10−19 = 1wb = 1eV
The name electron volt arises from the fact that, if an
electron falls through a potential of one volt , its
potential energy will be
1.6 × 10−19 = 1wb
An electron volt is the amount of kinetic energy
gained or lost by a single electron accelerating
from rest through an electric potential
difference of one volt in vacuum.
Find the following:
1- Electrostatic force between electron and
proton.
2- If we assume electrostatic force equal to
centrifugal force find velocity if electron
revolving in this orbital.
Example 1
The electron and proton of a
hydrogen atom are separated (on
the average) by a distance of
about 5.3 × 10−11 𝑚
3- Electrical field produce by proton at
location of electron .
4- Acceleration of electron due to electric
field of proton.
5- Point location where electrical field is
maximum.
6- Potential energy of electron.
7- Potential difference between electron and
proton.
Example 2
Consider two parallel electrodes (A and B
as shown in figure (on the side) separated
a distance d and potential
different between them = ΔV. An electron
leaves the surface of plate A at t=0 with
initial velocity 𝑣 = 0 in direction toward B.
derive the equation of velocity in term of
distance 𝑥
Figure 4
Magnetic field
Magnetic Field
Explanation
In our study of electricity, we described
that an electric field surrounds any
electric charge. In addition to containing
an electric field, the region of space
surrounding any moving electric charge
also contains a magnetic field. A
magnetic field also surrounds a
magnetic substance making up a
permanent magnet.
The symbol B has been used to
represent a magnetic field. Note that the
plane that contain magnetic field is
always perpendicular on electric field
plane if the exit at same place.
𝐸⊥𝐵
Unit of magnetic field is the Tesla (T), also Tesla
equal to Weber per square meter (1T = Wb /m2).
Unit of Magnetic Field
In practice, the Tesla is very large unit for
magnetic field{conventional laboratory magnets
can produce magnetic fields as large as about
25µT - 2.5 𝑇
Superconducting magnets that can generate
magnetic fields as 30 T, have been constructed.
These values can be compared with the value of
Earth’s magnetic field near its surface, which is
about 0.5 G, or 0.5×10-4T }, the gauss (G), is
often used.
The gauss is related to the Tesla through the
conversion :
1𝐺 = 1 × 10−4 𝑇
Magnetic Field of
Moving Point Charge
If a charge moving with a
constant velocity in the
electrical and magnetic field
will generate as shown in Figure
below
Resketching Magnetic
Field of Moving Point
Charge
We can resketch the figure beside
by looking into front view . If
direction of velocity into the page
we use crosses (×), representing the
tails of arrows. If direction of
velocity out of the page, we use
dots (.), representing the tips of
arrows.
Understanding
Magnetic Field lines
If charge was revolving in circular
path the magnetic fled will be as
drawn in Figure (a) and if charge
was revolving about it's self (spin)
the magnetic field will be as shown
in Figure (b)
Magnetic Field of
Electrical Current
Electrical current produce by moving
charge through conductor, therefore
any conductor carrying electrical
current will produce electric and
magnetic field as shown in figure
beside.
Force on Moving Charge
in Magnetic Field
If a charge 𝑞 moving with velocity 𝑣. It is
found experimentally that the strength of the
magnetic force on the particle is proportional
to the magnitude of the charge 𝑞, the
magnitude of the velocity 𝑣, the strength of
the external magnetic field 𝐵, and the sine of
the angle 𝜃 between the direction of the
velocity 𝑣, the strength of the external
magnetic field 𝐵
These observations can be summarized by
writing the magnitude of the magnetic
force as
𝐹 = 𝑞𝑣𝐵𝑆𝑖𝑛𝜃
Right Hand Rule
Note: To indicate the direction of 𝐵, we
use the following conventions:
· If is directed into the page we use a
series of crosses (×), representing the
Direction of Magnetic
Field (𝐵)
tails of arrows. If is directed out of the
page, we use a series of dots (.),
representing the tips of arrows.
Motion of
charge in
magnetic
field
Motion of charge in magnetic field
Case One:
If the direction of the particle’s velocity is perpendicular to the field ,
as in Figure on the side . Application of the right-hand rule at any
point shows that the magnetic force is always directed toward the
center . The force causes the particle to alter its direction of travel
and to follow a circular path with radius =r
𝑞𝑣𝐵 =
𝑟=
𝑚
𝑟
𝑚
𝑞𝑣𝐵
This Equation is often called the cyclotron equation, because it’s used in
the design of these instruments (popularly known as mass spectrometer)
Case Two
If the initial direction of the
velocity of the charged particle is
not perpendicular to the magnetic
field, as shown in Figure below.
The path followed by the particle is
a spiral (called a helix) along the
magnetic field lines.
Case Three
Suppose a uniform magnetic field exists in a finite region
of space. If a charged particle be injected into this region
from the outside and direction of the particle’s velocity is
perpendicular to the field.
The path of a particle for which the force is always
perpendicular to the velocity is a circle. The particle
therefore follows a circular arc and exits the field on
the other side of the circle, as shown
in Figure on the side, for a particle with constant kinetic
energy
Charged Particles
Moving in Electric
and Magnetic
Fields
𝐹𝑡𝑜𝑡𝑎𝑙 = 𝐹𝐸 + 𝐹𝑀
Where:
In general
𝐹𝐸 = 𝑞𝐸
Is the force due electrical field
𝐹𝑀 = 𝑞𝑣𝐵 Is the force due magnetic field
𝐹𝑡𝑜𝑡𝑎𝑙 = 𝑞𝑣𝐵 Is the directional sum
Velocity
selector
Velocity Selector
It contains a source produce charge
q with velocity v and injected it
through slit containing a uniform
electric field perpendicular to a
uniform magnetic field as shown in
figure by the side.
When the force due to the electric field is
equal but opposite to the force due to the
magnetic field the particle moves in a
straight line
On Velocity Selector
This device used when all the
particles need to move with the
same velocity regardless there
mass and charge
Mass
Spectrometer
More on Mass
spectrometer
As shown in Figure to the
side, ions are produced by
heating or electrical current
then the accelerated by
potential different V that
made potential energy of
ion converted into kinetic
energy
1
𝑚𝑣 2 = 𝑞𝑉
2
To be continued