5 ELECTRICIT Y
AND MAGNETISM
Introduction
• Introduction Modern society uses a whole range of electrical devices
from the simplest heated metal filaments that provide light, through
to the most sophisticated medical instruments and computers.
Devices of increasing technical complexity are developed every day.
• In this topic we look at the phenomenon of electricity, and what is
meant by charge and electric current. We consider the three effects
that can be observed when charge flows in an electric circuit.
• Understanding:
• ➔ Charge
• ➔ Electric field
• ➔ Coulomb’s law
• ➔ Electric current
• ➔ Direct current (dc)
• ➔ Potential difference (pd)
Electric Fields
• https://www.youtube.com/watch?time_continue=393&v=19B4LHWG
73g
• https://www.youtube.com/watch?time_continue=230&v=MuYvvzQb
D1o
• https://www.youtube.com/watch?time_continue=314&v=Qcf9OFBAe
Yw
Explaining electrostatics
• https://courses.edx.org/courses/RiceX/PHYS102.1x/2015T1/coursew
are/d029e83e48314bebb1697e0d0e754c3d/8943cc9f86934797b044
99e3759308ba/1?activate_block_id=i4x%3A%2F%2FRiceX%2FPHYS10
2.1x%2Fvertical%2F6f52ab065a9243b6921c03184f110f3c
• https://courses.edx.org/courses/RiceX/PHYS102.1x/2015T1/coursew
are/d029e83e48314bebb1697e0d0e754c3d/38f98f40cb91428fa9877
b982c1f89f0/2?activate_block_id=i4x%3A%2F%2FRiceX%2FPHYS102.
1x%2Fvertical%2Fe3e8cf815a60417fbc4e494551a53fe7
Measuring and defining charge
• The unit of charge is the coulomb (abbreviated to C). Charge is a
scalar quantity.
• The coulomb is defined as the charge transported by a
current of one ampere in one second.
• All electrons are identical,
with each one having a
charge equal to 𝟏. 𝟔 ×
𝟏𝟎−𝟏𝟗 𝑪; this fundamental
amount of charge is known
as the electronic charge or
elementary charge and
given the symbol e.
𝑒 − = 𝟏. 𝟔 × 𝟏𝟎−𝟏𝟗 𝑪
Forces between charged objects
• In 1785, Coulomb published the first of several Mémoires in which he
reported a series of experiments that he had carried out to
investigate the effects of forces arising from charges.
• He found, experimentally, that the force between two point charges
1
separated by distance r is proportional to 2 .
𝑟
• The equation as it stands applies only for charges that are in a
vacuum. If the charges are immersed in a different medium then the
value of the permittivity is different.
• It is usual to amend the equation slightly too, k becomes 1/4πε as the
“0” subscript in 𝜀0 should only be used for the vacuum case.
Electric fields
• Sometimes the origin of a force
between two objects is obvious
(physical contact), an example is
the friction pad in a brake
rubbing on the rim of a bicycle
wheel to slow the cycle down. In
other cases there is no physical
contact between two objects
yet a force exists between them.
• Such forces are said to “act at a distance”.
• The term field is used in physics for cases where two separated objects exert forces
on each other.
• We say that in the case of the comb picking up the paper, the paper is sitting in the
electric field due to the comb.
`
What is a vector field?
• Is an assignment of a vector to
each point in a region of space.
• The idea of field lines was first introduced by Michael Faraday
• They are useful for illustrating and understanding the nature of a
particular field
There are some conventions for drawing these electric field patterns:
● The lines start and end on charges of opposite sign.
● An arrow is essential to show the direction in which a positive charge
would move (i.e. away from the positive charge and towards the
negative charge).
● Where the field is strong the lines are close together. The lines act to
repel each other.
● The lines never cross.
● The lines meet a conducting surface at 90°
The density of field lines
in a region of space is
proportional to the
strength of the field at
that point
Electric field lines demo
• https://www.youtube.com/watch?v=joJ9qalPlFQ
• https://www.youtube.com/watch?v=7vnmL853784
Electric field strength
• As well as understanding the field pattern, we need to be able to
measure the strength of the electric field.
• The electric field strength is defined using the concept of a positive
test charge.
• A formal definition for electric field strength at a point is the force
per unit charge experienced by a small positive point charge placed
at that point.
Common
electric field
patterns
Vector addition of field strengths
Exercise: Find the electric field over the blue
particle due to the red ones.
Conductors
• In conducting materials such as copper, electric charges move readily
in response to the forces that electric fields exert.
• Once static equilibrium is established with all of the excess charge on
the surface, no further movement of charge occurs.
• At equilibrium under electrostatic conditions, any excess charge
resides on the surface of a conductor.
On the surface = no charge inside
no charge inside = No net electric
field inside the conductor
Net electric field = The sum of all the electric fields
E = external electric field
E’ = Induced Electric Field
At equilibrium,
Induced Field E’ = External Field E
Conducting sphere with a net charge
• The field outside the
sphere appears exactly
the same as that of the
point charge.
Close to a conductor
• First of all, if we are close enough then the surface
will appear flat.
• Secondly we would see that all the free electrons
are equally spaced. Forces stabilize until they find
equilibrium (symmetric positions).
• Parallel to the surface, electric field components all
cancel out with each other so there is no electric
field in this direction
Tear-drop-shaped
piece of metal
Conduction in metals
• The metal atoms in a solid are bound together by the metallic bond.
• This means that electrons are donated from the outer shells of the
atoms to a common sea of electrons that occupies the entire volume
of the metal.
These free electrons are called conducting electrons
Electric current
• When you connect a battery to a conducting wire charge flows
through it. This flowing of charge is called current.
• Current is measured in amperes, the symbol for the unit is A.
• The ampere is a fundamental unit defined as part of the SI.
How much charge flows through a certain
point in a certain interval of time.
In each cycle
72nC are
transferred
Charge flow is not that simple!
• https://www.youtube.com/watch?v=qg0JY4GNK0w
• Electrons should have a Maxwellian speed distribution somewhat like
that of the molecules in a gas. For copper, the effective speed of
𝑚
6
electrons is 𝑣𝑒𝑓𝑓 = 1.6 × 10 .
𝑠
Net displacement
Charge carrier drift speed
Conduction in gases and liquids
• Corona Discharge
• https://www.youtube.com/watch?v=2pLJ2ZX4By4
• Van de Graaff generator
• https://www.youtube.com/watch?v=ubZuSZYVBng
Electric Potential
When the body is charged, either electrons are supplied to it, or they are
removed from it. In both the cases, the work is done. This work is stored in the
body in the form of electric potential. Thus, the body can do the work by
exerting a force of attraction or repulsion on the other charged particles.
The electrical potential is defined as the amount of work needed to move a unit
of positive charge from a reference point to a specific point.
Electric Potential Difference
The electrical potential difference is defined as the amount of work
done to carry a unit charge from one point to another in an electric
field. In other words, the potential difference is defined as the
difference in the electric potential of the two charged body.
• When a body is charged to a different
electric potential as compared to the other
charged body, the two bodies are said to
have a potential difference.
A simple circuit will illustrate these ideas:
• When the switch is closed,
electrons flow round the
circuit.
• Notice the direction in which
the electrons move and also
that the diagram shows the
direction of a conventional
current.
• The two directions are
opposite; in this case,
clockwise for the electron
flow and anti-clockwise for
the conventional current.
Electromotive force (emf)
• There is no force, this is just wrong name for the concept.
• When charge flows electrical energy can go into another form such as
internal energy (through the heating), or it can be converted from another
form (for example, light (radiant energy) in solar (photovoltaic) cells).
• The term emf will be used in this course when energy is transferred to the
electrons in, for example, a battery.
• The term potential difference will be used when the energy is transferred
from the electrical form into, for example, motion energy.
Long story short:
An EMF is just a
power source
Power, current, and pd
• how much energy is delivered to a conductor by the electrons as they
move through it?
• Suppose there is a conductor with a potential difference V between
its ends when a current I is in the conductor.
• In time Δt the charge Q that moves through the conductor is equal to
I Δt.
• The energy W transferred to the conductor from the electrons is QV
which is (IΔt)V.
• So the energy transferred in time Δt is W = IVΔt
• The electrical power being supplied to the conductor is
energy/time = W/∆t.
• Therefore
• Electrical power  P = IV
• P = IV is known a Joule’s
Law
• It refers to the power
transferred per unit
current in a conductor.
The electronvolt
Definition
Useful links
• http://demo.webassign.net/ebooks/cj6demo/pc/c18/read/main/c18x
18_8.htm
• https://electricalbaba.com/why-electric-field-inside-a-conductor-iszero/
• https://www.physicsclassroom.com/class/estatics/Lesson-4/ElectricField-Lines
• http://ch301.cm.utexas.edu/imfs/#solids/metallic-solids.html
Eclipse lunar
¿Por qué la Luna se ve naranja y rojiza
durante un eclipse lunar?
La razón es que la Luna atraviesa por la
sombra de la Tierra, la cual se divide en dos
partes: penumbra y umbra. En la umbra, la
luz del Sol que atraviesa la atmósfera
terrestre se dispersa (se separan sus colores
como al atravesar un prisma), de los cuales
el rojo es el que más se desvía de su
dirección original. Al observar un eclipse
total, primero la Luna se oscurece (pasa por
la penumbra) para después tomar
coloraciones amarillosas-naranjas y rojas
durante la totalidad del eclipse. Pasando
este momento, las tonalidades ocurren en
forma inversa: naranjas, amarillos y
oscurecimiento de la Luna al pasar a la otra
zona de penumbra, terminando de esta
forma el eclipse total de Luna.