Kurdistan Regional Governmental-Iraq

Ministry of Higher Education and

Scientific Research, University of Duhok

College of Science , Department of Physics

Electricity & Magnetism

A report submitted to the Department of Physics

College of Science, University of Duhok

As a requirement for the final exam

Student Name:
Moodle Email:

Year:

Course Name:

Instructor:

Date:
TABLE OF CONTENTS
INTRODUCTION OF CURRENT AND RESISTANCE.............................................2
WHAT IS PHYSICS?.................................................................................................2
BACKGROUND........................................................................................................3
CURRENT.................................................................................................................3
WHAT IS THE RELATION BETWEEN CURRENT AND RESISTANCE?................4
HOW DO YOU CALCULATE CURRENT AND RESISTANCE?...............................5
THE DIRECTION OF A CURRENT..........................................................................5
RESISTORS IN PARALLEL......................................................................................6
RESISTORS IN SERIES AND PARALLEL...............................................................7
VOLTAGE, CURRENT, AND RESISTANCE...........................................................10
JOULE’S LAW.........................................................................................................11
JOULE’S LAW OF HEATING..................................................................................11
JOULES LAW OF HEATING EFFECT OF CURRENT...........................................11
CONCLUSION........................................................................................................12
SOURCES..............................................................................................................12
INTRODUCTION OF CIRCUIT...............................................................................13
SWITCH CIRCUIT..................................................................................................13
ELECTROMOTIVE FORCE....................................................................................14
THE CIRCUIT EQUATION......................................................................................14
ALTERNATE DEFINITION OF ELECTROMOTIVE FORCE..................................15
SOURCES..............................................................................................................15
INTRODUCTION.....................................................................................................16
MAGNETIC FIELD..................................................................................................17
RIGHT HAND RULE 1............................................................................................18
CONCLUSION........................................................................................................20
SOURCES..............................................................................................................21
INTRODUCTION OF MAGNETIC FIELDS DUE TO CURRENTS.........................22
BACKGROUND......................................................................................................22
ELECTRIC CURRENTS AND MAGNETIC FIELDS...............................................22
SOURCES..............................................................................................................23

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INTRODUCTION OF CURRENT AND RESISTANCE

Current can be changed by increasing or decreasing the voltage of the circuit.

Current is a measure of the rate of flow of electric charge through a circuit. ... A
fixed resistor has a resistance that remains the same. Many domestic appliances
use resistance to transfer electrical energy to heat and light energy. Resistance
Any device in a circuit which converts electrical energy into some other form
impedes the current. The device which converts electrical energy to heat energy
is termed a resistor and its ability to impede current is termed resistance. So,
resistance can be defined as the opposition to current caused by a resistor.
Current tends to move through the
conductors with some degree of
friction, or opposition to motion.
This opposition to motion is more
properly called resistance. The
amount of current in a circuit
depends on the amount of voltage
and the amount of resistance in the
circuit to oppose current flow.

BACKGROUND

CURRENT

Under the influence of this field the free electrons in the wire experi- cnce a
force in the opposite direction to the field and accelerate in the direction of this
force. (The other electrons, as well as the positive nuclei, are also acted on by
the field but are prevented from accelerating by the binding forces which hold
these electrons to the nuclei and hold the nuclei together to form a solid body.)

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Collisions with the stationary particles in the metal very soon slow down the
free electrons or stop them. After which
they again accelerate, and so on.
Succession of accelerations and
decelerations, but they will acquire a
certain average velocity in the opposite
direction to the field and we may assume
that they all move steadily with this
average velocity. The free electrons also share in the thermal energy of the
conductor, but their thermal motion is a random one and for our present
purposes may be ignored. Fig. 1-1 illustrates a portion of a wire in which there is
a field toward the left and consequently a motion of free electrons toward the
right. Each electron is assumed to move with the same constant velocity. And in
time di each advances a distance v dt. In this time, the number of electrons
crossing any plane such as the one shown shaded, is the number contsined in a
section of the wire of length v dt or volume Av dt, where A is the cross section of
the wire. If there are n free electrons per unit volume, the number crossing the
plane in time dt is nAv dt, and if e rep- resents the charge of each, the total
charge crossing the area in time di is

dq =nevA dt

The rate al which charge is transporled across a seclion of the wire, or dg/dt, is
called the current in the wire. Current is represented by the letter i (or I).

i = dq/dt

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HOW DO YOU CALCULATE CURRENT AND RESISTANCE?

By Ohms Law and Power:

• To find the Voltage, ( V ) [ V = I x R ] V (volts) = I (amps) x R (Ω)

• To find the Current, ( I ) [ I = V ÷ R ] I (amps) = V (volts) ÷ R (Ω)

• To find the Resistance, ( R ) [ R = V ÷ I ] R (Ω) = V (volts) ÷ I (amps)

• To find the Power (P) [ P = V x I ] P (watts) = V (volts) x I (amps)

THE DIRECTION OF A CURRENT

Infinitesimal area dA across which the current is di, and defines the current
density as di J= di/dA It is of interest to estimate the average velocity of the
free electrons in a conductor in which there is a current.

Consider a copper conductor 1 cm in diameter in which the current is 200 amp.

The current density is.

J= i/A = 200/1/4Π(0.1)²

=2.54*10<6 amp/m²

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Previous calculations. Have shown that there are in copper about 8.5 X 10” free
electrons/cm’ or 8.5 X 10 free electrons/m’. Then since J= nev

V=J/ne = 2.54 *10<6/8.5*10<28*10<-19

=1.9*10<-4 m/sec

or about .02 en/see. The velocity is therefore quite small. The average velocity
of the free electrons in a conductor should not be confused with the velocity of
propagation of electromagnetic waves in free space, which is 3 x 10<8 m/sec or
186,000 mi/sec.

RESISTORS IN SERIES AND PARALLEL

Resistors can be connected together in an unlimited number of series and

parallel combinations to form complex resistive circuits. In the previous tutorials
we have learnt how to connect individual resistors together to form either a
Series Resistor Network or a Parallel Resistor Network and we used Ohms Law
to find the various currents flowing in and voltages across each resistor
combination. But what if we want to connect various resistors together in
“BOTH” parallel and series combinations within the same circuit to produce
more complex resistive networks, how do we calculate the combined or total

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circuit resistance, currents and voltages for these resistive combinations.

Resistor circuits that combine series and parallel resistors networks together are
generally known as Resistor Combination or mixed resistor circuits. The
method of calculating the circuits equivalent resistance is the same as that for
any individual series or parallel circuit and hopefully we now know that resistors
in series carry exactly the same current and that resistors in parallel have exactly
the same voltage across them. For
example, in the following circuit
calculate the total current ( IT ) taken
from the 12v supply. At first glance this
may seem a difficult task, but if we
look a little closer we can see that the
two resistors, R2 and R3 are actually
both connected together in a “SERIES”
combination so we can add them together to produce an equivalent resistance
the same as we did in the series resistor tutorial. The resultant resistance for this
combination would therefore be;

R2 + R3 = 8Ω + 4Ω = 12Ω

So, we can replace both resistor R2 and R3 above with a single resistor of
resistance value 12Ω

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So, our circuit now has a single resistor RA in “PARALLEL” with the resistor
R4. Using our resistors in parallel equation we can reduce this parallel
combination to a single equivalent resistor value of R(combination) using the
formula for two parallel connected resistors as follows.

The resultant resistive circuit now looks something like this:

We can see that the two remaining resistances, R1 and R(comb) are connected
together in a “SERIES” combination and again they can be added together
(resistors in series) so that the total circuit resistance between points A and B is
therefore given as:

Thus, a single resistor of just 12Ω can be used to replace the original four
resistors connected together in the original circuit above.

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JOULE’S LAW

Joule's first law states that the heat produced by current in a conductor is directly
proportional to the square of the current , the resistance of the conductor , and
the time for which the current exists .the principle that the rate of production of
heat by a constant direct current is directly proportional to the resistance of the
circuit and to the square of the current. The principle that the internal energy of a
given mass of an ideal gas is solely a function of its temperature.

JOULE’S LAW OF HEATING

Joule's law of heating states that when a current 'i ' passes through a conductor
of resistance 'r' for time 't' then the
heat developed in the conductor
is equal to the product of the
square of the current, the
resistance and time. H = i 2 rt.

JOULES LAW OF HEATING EFFECT OF CURRENT

This law governs the heating effect of current as heat energy released by a
conductor when current passes through it. If the conductor is having resistance R

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and current, I passes through it for time t, the heat energy dissipated, Q = I^2 X
RXt

CONCLUSION

Ohm’s Law deals with the relationship between voltage and current in an ideal
conductor. This relationship states that: The potential difference (voltage) across
an ideal conductor is proportional to the current through it. The constant of
proportionality is called the “resistance”, R. This can be expressed in an
equation as V=IR and can be manipulated to find the other two variables. (I and
R) The point of graphing this lab experiment was to establish the relationship
between current and voltage in part I and the relationship between current and
resistance in part II.

SOURCES

• Google :

• https://www.coursehero.com/file/19062144/conclusion-Ohms-law-lab/

• https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/voltage-
current-resistance-relate/

• https://www.electronics-tutorials.ws/resistor/res_4.html

• https://www.electronics-tutorials.ws/resistor/res_5.html

• Book’s name : FUNDAMENTAL University Physic

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INTRODUCTION OF CIRCUIT

The Definition of Electrical Circuits An electrical circuit is a closed loop of

conductive material that allows electrons to flow through continuously without
beginning or end. There is continuous electrical current goes from the supply to
the load in an electrical circuit. An electrical circuit is a closed loop of
conductive material that allows electrons to flow through continuously without
beginning or end. There is
continuous electrical current goes
from the supply to the load in an
electrical circuit. People also say
that a complete path, typically
through conductors such as wires
and through circuit elements, is
called an electric circuit. An
electrical circuit is an electrical device that provides a path for electrical current
to flow. After you get the definition of the electrical circuit, now we are going to
show you three simple electrical circuits. Switch Circuit

SWITCH CIRCUIT
A switch is a device for making and breaking the connection in an electric
circuit. We operate switches for lights, fans, electric hair drier and more many
times a day but we seldom try to see the
connection made inside the switch circuit. The
function of the switch is to connect or complete
the circuit going to the load from the supply. It
has moving contacts which are normally open.

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With a switch you can turn the device on or off, therefore, it is a very important
component in an electrical circuit.

ELECTROMOTIVE FORCE

In electromagnetism and electronics, electromotive force, is the electrical action

produced by a non-electrical source. Devices provide an emf by converting other
forms of energy into electrical energy, such as batteries or generators.
Sometimes an analogy to water pressure is used to describe electromotive force.

THE CIRCUIT EQUATION

calculate circuits : B The total current in the circuit can be calculated by

dividing the supply voltage E by the total resistance of the circuit or by
calculating all the currents in any parallel bank and adding them together, or
dividing the volt drop across any series resistor by its resistance. At the most
basic level, analyzing circuits involves calculating the current and voltage for a
particular device. ... One of the most important device equations is Ohm’s law,
which relates current (I) and voltage (V) using resistance (R), where R is a
constant: V = IR or I = V/R or R = V/I.

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ALTERNATE DEFINITION OF ELECTROMOTIVE FORCE

Electromotive force, abbreviation E or emf, energy per unit electric charge that
is imparted by an energy source, such as an electric
generator or a battery. The work done on a unit of
electric charge, or the energy thereby gained per unit
electric charge, is the electromotive force. Called
electromotive force Electromotive Force.
Electromotive force (emf) is a measurement of the
energy that causes current to flow through a circuit. It
can also be defined as the potential difference in
charge between two points in a circuit. Electromotive
force is also known as voltage, and it is measured in
volts.

SOURCES

• https://www.britannica.com/science/electromotive-force
• https://www.chegg.com/homework-
help/definitions/electromotive-force-4
• https://en.m.wikipedia.org/wiki/Electromotive_force
• https://www.dummies.com/education/science/science-
electronics/circuit-analysis-for-dummies-cheat-sheet/
• Book’s name : FUNDAMENTAL University Physic

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INTRODUCTION

This section provides background information on magnetic fields with reference

to electron microscopes and similar instruments. Magnetic fields are created by
electric currents in the space around where the currents flow. Currents which do
not change with time (called direct currents or DC) make constant magnetic
fields which we call DC fields. A gradual change in a direct current creates a
corresponding gradual change in the DC field. By convention we refer to
unchanging fields and fields which change in this slow non-periodic manner as
DC fields. Currents which change sign in a regular manner with time are called
alternating currents or AC and give rise to corresponding AC magnetic fields.
The most common AC fields are created by power lines and usually have
fundamental frequencies of 50 or 60 Hz
(referred to as “line” frequency) often with
harmonics up to about 5 kHz. AC fields at
other frequencies may be generated by
rotating machines containing permanent
magnets. Examples are magnetic stirrers and
plasma etch machines which may make fields
at about 0.3 Hz. The units used to measure
magnetic fields are as follows.... SI unit of
magnetic field strength:
Amp/metre (A/m)
SI unit of magnetic flux density: Tesla (T)
CGS unit of magnetic flux density: Gauss (G)

MAGNETIC FIELD

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A magnetic field is a vector field that describes the magnetic influence of

electric charges in relative motion and magnetized materials. ... Magnetic fields
surround and are created by magnetized material and by moving electric charges
(currents) such as those used in electromagnets.

How is a magnetic field created?

As Ampere suggested, a magnetic field is produced whenever an electrical

charge is in motion. The spinning and orbiting of the
nucleus of an atom produces a magnetic field as does
electrical current flowing through a wire. The direction of
the spin and orbit de termini the direction of the
magnetic field.

Force on a moving charge

Magnetic Forces on Moving Charges The magnetic force on a free moving

charge is perpendicular to both the velocity of the charge and the magnetic field
with direction given by the right-hand rule. The force is given by the charge
times the vector product of velocity and magnetic field.

Which equation gives the force for a charge moving through a magnetic
field?
We are given the charge, its velocity, and the magnetic field strength and
direction. We can thus use
the equation F = qvB sin θ
to find the force.

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What is Q in F qvB?

Magnetic Force The force is perpendicular to both the velocity v of the charge q
and the magnetic field B. 2. The magnitude of the force is F = qvB sinθ where θ
is the angle < 180 degrees between the velocity and the magnetic field.

What does Q mean in physics?

Q is the symbol used to represent charge, while n is a positive or negative

integer, and e is the electronic charge, 1.60 x 10-19 Coulombs.

RIGHT HAND RULE 1

The magnetic force on a moving charge is one of

the most fundamental known. Magnetic force is as
important as the electrostatic or Coulomb force. Yet
the magnetic force is more complex, in both the
number of factors that affects it and, in its direction,
than the relatively simple Coulomb force. The
magnitude of the magnetic force F on a charge q
moving at a speed v in a magnetic field of strength
B is given by
F = qvB sin θ,
where θ is the angle between the directions of v and
B. This force is often called the Lorentz force. In fact, this is how we define the
magnetic field strength B—in terms of the force on a charged particle moving in
a magnetic field. The SI unit for magnetic field strength B is called the tesla (T)
after the eccentric but brilliant inventor Nikola Tesla (1856–1943). To determine
how the tesla relates to other SI units, we solve F = qvB sin θ for B.
B=FqvsinθB=Fqvsinθ
Because sin θ is unitless, the tesla is 1 T=1 N C⋅ m/s=1 NA⋅ m1 T=1 N C⋅
m/s=1 NA⋅ mm (note that C/s = A). Another smaller unit, called the gauss (G),
where 1 G = 10−4 T, is sometimes used. The strongest permanent magnets have
fields near 2 T; superconducting electromagnets. may attain 10 T or more. The
Earth’s magnetic field on its surface b only about 5 × 10−5 T, or 0.5 G.
The direction of the magnetic force F is perpendicular to the plane formed by v
and B, as determined by the right-hand rule 1 (or RHR-1), which is illustrated
in Figure 1. RHR-1 states that, to determine the direction of the magnetic force

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on a positive moving charge, you point the thumb of the right hand in the
direction of v, the fingers in the direction of B, and a perpendicular to the palm
points in the direction of F. One way to remember this is that there is one
velocity, and so the thumb represents it. There are many field lines, and so the
fingers represent them. The force is in the direction of you would push with your
palm. The force on a negative charge is in exactly the opposite direction to that
on a positive charge.

Magnetic force can cause a charged particle to move in a circular or spiral path.
Cosmic rays are energetic charged particles in outer space, some of which
approach the Earth. They can be forced into spiral paths by the Earth’s magnetic
field. Protons in giant accelerators are kept in a circular path by magnetic force.
The bubble chamber photograph in this figure shows charged particles moving
in such curved paths. The curved paths of
charged particles in magnetic fields are
the basis of a number of phenomena and
can even be used analytically, such as in
a mass spectrometer. Figure Trails of
bubbles are produced by high-energy
charged particles moving through the
superheated liquid hydrogen in this
artist’s rendition of a bubble chamber.
There is a strong magnetic field
perpendicular to the page that causes the
curved paths of the particles. The radius
of the path can be used to find the mass, charge, and energy of the particle. So
does the magnetic force cause circular motion? Magnetic force is always
perpendicular to velocity, so that it does no work on the charged particle. The
particle’s kinetic energy and speed thus remain constant. The direction of motion
is affected, but not the speed. This is typical of uniform circular motion. The
simplest case occurs when a charged particle moves perpendicular to a uniform
BB -field, such as shown in Figure . (If this takes place in a vacuum, the
magnetic field is the dominant factor determining the motion.
( Fc=mv2/rFc=mv2/r. Noting that sinθ=1sinθ=1, we see that F=qvBF=qvB.

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figure . A negatively charged particle moves in the plane of the page in a region
where the magnetic field is perpendicular into the page (represented by the small
circles with x’s—like the tails of arrows). The magnetic force is perpendicular to
the velocity, and so velocity changes in direction but not magnitude. Uniform
circular motion results. Because the magnetic force FF supplies the centripetal
force FcFc, we have qvB=qvB= mv2r.mv2r. Solving for rr yields
r=r= mvqB.mvqB. Here, rr is the
radius of curvature of the path of a
charged particle with mass mm and
charge qq, moving at a speed vv
perpendicular to a magnetic field of
strength BB. If the velocity is not
perpendicular to the magnetic field,
then vv is the component of the
velocity perpendicular to the field. The
component of the velocity parallel to
the field is unaffected, since the magnetic force is zero for motion parallel to the
field. This produces a spiral motion rather than a circular one.

CONCLUSION

When I started this project I initially had the intention to model the magnetic
fields due to a cylinder, bar magnet, and sphere. Little did I realize that while I
knew that these fields should look like theoretically, modelling them would have
been a great undertaking. The fields due to a bar
magnet is that of a magnetic dipole and that in itself
seemed as though it would have been a project. The
sphere could have been modeled in two different
ways: as a rotating sphere of charge, or a collection
of current-carrying loops. Both were very difficult
to find the magnetic field for at any given point and
so I was at a loss for things to model. I was only
able to successfully plot the magnetic field due to a
line of charge rather than a cylinder since I was
having trouble making Mathematica plot piecewise
vector functions.

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SOURCES

Google
•https://en.m.wikiversity.org/wiki/Physics_equations/Magn
etic_field_calculations
• https://openstax.org/books/college-physics/pages/22-5-
force-on-a-moving-charge-in-a-magnetic-field-examples-
and-applications
• https://en.m.wikipedia.org/wiki/Magnetic_field
•https://www.ndeed.org/EducationResources/HighSchool/
Magnetism/fieldcreation.htm
• https://courses.lumenlearning.com/boundless-
physics/chapter/magnetic-force-on-a-moving-electric-
charge/

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INTRODUCTION OF MAGNETIC FIELDS DUE TO CURRENTS

A current traveling through a loop of wire creates a magnetic field along the axis
of the loop. The direction of the field inside the loop can be found by curling the
fingers of the right hand in the direction of the current through the loop; the
thumb then points in the direction of the magnetic field .Electric current
produces a magnetic field. This magnetic field can be visualized as a pattern of
circular field lines surrounding a wire. ... Magnetic Field Generated by Current:
(a) Compasses placed near a long straight current-carrying wire indicate that
field lines form circular loops centered on the wire.

BACKGROUND

ELECTRIC CURRENTS AND MAGNETIC FIELDS

An electric current will produce a magnetic field, which can be visualized as a

series of circular field lines around a wire segment.
Electric current produces a magnetic field. This
magnetic field can be visualized as a pattern of circular
field lines surrounding a wire. One way to explore the
direction of a magnetic field is with a compass, as
shown by a long straight current-carrying wire in. Hall
probes can determine the magnitude of the field.
Another version of the right-hand rule emerges from
this exploration and is valid for any current segment—
point the thumb in the direction of the current, and the
fingers curl in the direction of the magnetic field loops
created by it. The equation for the magnetic field
strength (magnitude) produced by a long straight
current-carrying wire is:
B=μ0I2πrB=μ0I2πr
For a long straight wire where I is the current, r is the shortest distance to the
wire, and the constant 0=4π10−7 T⋅m/A is the permeability of free space. (μ0 is
one of the basic constants in nature, related to the speed of light. ) Since the wire
is very long, the magnitude of the field depends only on distance from the wire
r, not on position along the wire. This is one of the simplest cases to calculate
the magnetic field strenght from a current.

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Ampere’s Law

You can think of the “surface” as the cross-sectional area of a wire carrying
current. The mathematical statement of the law states that the total magnetic
field around some path is directly proportional to the current which passes
through that enclosed path.

Magnetic field due to current carrying wire

Magnetic field due to current in straight wire Magnetic field on the perimeter of
circle is tangential. ... Right hand thumb rule If holding straight wire with right
hand so that the extended thumb points in the direction of current, then curl of
the fingers gives the direction of magnetic field around the straight wire.

SOURCES

• https://courses.lumenlearning.com/boundless-
physics/chapter/magnetism-and-magnetic-fields/
• https://cnx.org/contents/5013e8fb-1b98-4325-b182-
bd5dfa78741b:416f27b6-e016-47c5-b1f1-01f470fd2907
• https://courses.lumenlearning.com/boundless-
physics/chapter/magnetism-and-magnetic-fields