Electromagnetic Devices: Principles, Concepts, and Applications

This report provides an in-depth discussion on the principles, concepts, and applications of electromagnetic devices. It covers topics such as scalar and vector fields, Coulomb's law, Gauss law, permanent and electromagnets, and their practical implementations. Numerical examples are also included to illustrate the concepts. The report is relevant for students studying electromagnetism or anyone interested in understanding the working of electromagnetic devices.

Electromagnetic devices

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
1. Scalar and vector fields ...........................................................................................................1
2. Coulomb's law .........................................................................................................................2
Vector form of coulombs-law......................................................................................................3
3. Gauss law ................................................................................................................................5
4. Permanent and electromagnets ...............................................................................................8
5. Bio- Savart law .......................................................................................................................9
6. Ampere force law ..................................................................................................................10
7. Toroisal coil ..........................................................................................................................11
CONCLUSION .............................................................................................................................13
REFERENCES .............................................................................................................................14

INTRODUCTION
Electromagnetic devices are based upon the principles of electric and magnetic
interaction as varying electric fields produces magnetic field and vice versa. The report will
discuss the various concepts and laws on which electromagnetic devices work upon.
1. Scalar and vector fields
Scalar quantities are defined as the entities which are characterised by magnitude only
and does not have any specific direction. On the other hand vector quantitate are known to be
entities with both direction and magnitude. For instance quantities like electric charge, distance
and mass are called scalar while velocity, displacement and magnetic fields are vectors (Jiles,
2015). In electromagnetic theory fields are defined as the quantities which are function of
position and may also depends upon time or other customised variables.
On the basis of nature of quantities fields are classified as scalar or vector fields. For
example temperature is scalar quantity and temperature distribution in any rod is scalar field
because at every point in the specified region of rod scalar function has defined value. Similarly,
in velocity filed of moving object at every location value of vector function is defined so that the
entire region is known as vector field.
Use and practical implementation:
Both scalar and vector fields are employed and analysed for variety of applications and
purpose. Vector fields are used in modelling the directional and magnitude aspects of fluids or
the physical quantities such as force or velocity. These fields are also an integral part of integral
and differential calculus (Tran, 2018). For instance this usage of vector field is implemented in
determining work done, interpretation of energy conservation, flow rotation (curl) and changes in
fluid flow volume (divergence). Along with the vectors, scalar fields are also used in quantum
theory and to underpin the applications based upon theory of relativity.
The distribution of scalar quantities such as spin zero, temperature and pressure
distribution within space or different objects be determined only with the application of scalar
and vector operations. The fields such as electric potential or gravitational forces cannot be
described without discussion of implementation of scalar and vector fields. The scalar quantities
are used in meteorology while the vector fields find their application in the electromagnetic
devices (Farrow, 2019).
Numerical example:
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To determine the maximum rate of change in any scalar quantity in a particular direction
gradient of scalar quantity is used. For instance the maximum change in function z= 4x²+ siny
+6z can be calculated by determining its gradient as follows:
Gradient z= z = (∂z/∂x)i + (∂z/∂y)j +(∂z/∂z)k∇
On substituting value of z we get:
z = 8xi +(cosy)j + 6k∇
Similarly, the divergence of any vector quantity can help to find the density variations at any
point. For instance the fluid flow of any liquid represented by vector field equation
u= 4xi + 12y³j +8z²k then its divergence can be calculated by the following formula.
Divergence u= .u = (∂u/∂x)i + (∂u/∂y)j +(∂u/∂z)k∇ (Zohuri, 2019)
.u = 4+ 36y² + 16z∇
This magnitude of this obtained vector provides the maximum change in density.
In this way various operations of scalar and vector quantities helps to determine the rotational
and linear motion properties of physical quantities.
2. Coulomb's law
Coulomb's law is defined as the law which describes the electrostatic force between two
electrically charged objects or particles. As per this law similar charges repels each other while
for the opposite charges attracting forces are present. This attractive or repulsive force acts along
the separation line between the charges. Thus, in conclusive statement Coulomb's law states that
the magnitude of electrostatic force has direct proportional relation with the product of stationary
charges and is inversely proportional to the square of distance separating both the charges. It can
be represented by following equation in scalar form:
|F| = K[|q.q|] * r²
Where q and q are the magnitude of charges, K is the coulomb's constant and is
approximately equals to 9*10 Nm² C-² and r is the distance between both the charges (Greaves
and et.al., 2018).
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(Source: Coulomb's law, 2019)
Vector form of coulombs-law
(Source: Electric charges and fields, 2019)
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Illustration 1: Coulomb's law (scalar form)
Illust
ration 1: Coulomb's law (vector form)

The electrostatic forces between charges located at position r1 and r2 can also be demonstrated
by Coulombs-law in the following format:
F1 = K[|q.q|] * [(r - r) / (r - r)³]
Practical implementation and applications:
The principles of electrostatic forces are widely used in printing and xerography
processes. Thus, law is used and practically applied in the functioning of Xerox and printing
machines. Though most of the applications of this law are indirect and rare but have great
significance. For instance protons within nucleus of atoms are held by strong repulsive forces
thus Coulomb's law is used to find that force so that electron transfer and reactions can be
understand and controlled (Chen, 2018). For explaining and utilising the various phenomenons
of quantum physics electrostatic forces are calculated using this law. Coulombs force is also
found to be the basic force which binds molecules of atoms and helps them to retain their solid or
liquid state. As compare to gravitational force, Coulomb's force is stronger but is usually not
visible.
Numerical examples:
Coulomb's force is used for analysing the behaviour and pattern of electrostatic forces by
calculating the forces between two charges. This can be understood by following examples.
When two forces of charge +4 mC and -5 mC are placed at distance of 30 mm in free space then
the force of attraction between both of these charges is equals to:
F= K[|q.q|] * r²
= (9*10) (-5* 10¯) (4* 10¯) / (0.03)²
F = -200 N
Example 2:
Three charges A, B, C of 1mC, 2mC and -3mC are placed on x axis. Distance between charge A
and B is 0.12 m and that between A and C is 0.42 m. Find the force on charge B?
F12 = K[|q.q|] * [(r - r) / (r - r)³]
F12 =(9*10) (1* 10¯) (2* 10¯)i / (0.12)² = +1.25i (repelled from charge A towards x axis)
Similarly,
F32 = K[|q.q|] * [(r - r) / (r - r)³]
F32= (9*10) (-3* 10¯) (2* 10¯)i / (0.3)² = +0.6i (attracted to charge C towards x axis)
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Thus, resultant force on charge B is = 1.25i +0.6i = 1.85N (In positive x direction)
3. Gauss law
Gauss law is defined as the theorem which gives the relation between electric charge
distribution to resulting electric field within a closed surface such as sphere or cylinder.
According to this law total electric flux within closed surface is equals to the ratio of charge
enclosed by the surface and the permittivity. Electric flux is known as the product of electric
field and surface area which is projected normally to electric field. Gauss law is applicable to
closed surface and allows the evaluation of enclosed charge by the method of electric field
mapping on surface exterior to charge distribution (Nousiainen and Koponen, 2017). Though
Gauss law can be used to find the electric field in variety of symmetical shapes but it cannot be
applied in some specific cases. For instance this law cannot provide the electric field caused by
electric dipoles.
Expression for the Gauss law: ϕ =q/ ϵ₀
Application:
This law is applied and is used to determine the electric fields when the electric charge is
distributed in a continuous pattern within symmetrical objects. Gauss law provides solution for
the complex electrostatic difficulties which can involve planar, spherical or cylindrical
symmetry. The law posses several forms and can be easily converted into differential equations
which makes it solution very easy and simplified. In various practical applications Gauss law
equations are used as solution for the Poission equation and Maxwell's four equations. Gauss law
is also used to find the electric field through various surfaces (Rothwell and Cloud, 2018). The
key applications of this use are as follows:
Electric field (E) due to infinity wire:
A wire with infinite length which has charge density and length as λ and L respectively.
The E can by assuming cylindrical surface is: E= λ/ 2Лrϵ₀
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(Source: Applications of Gauss’s Law, 2019)
E due to infinite plate sheet
For an infinite sheet E is perpendicular to plane and is given by the equation E = σ/2ϵ₀
where ϵ is the free space permittivity and σ is the surface charge density.₀
(Source: Applications of Gauss’s Law, 2019)
E due to spherical shell
The inward and outward E of a spherical surface of radius r and charge density σ is given
by the following expressions:
E inside sphere: q/ϵ₀
E outside sphere: kq/r
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Numerical example:
The Gauss law can be used solve various numerical problems related to electric filed,
flux and charge densities.
Example 1: A closed surface encloses three charges of value 3C, 5C and 6C respectively then the
total flux enclosed by the surface is:
Total charge q: 3C+ 5C+ 6C = 14C
By applying Gauss law:
net flux ϕ =q/ ϵ₀
= 14* (8.854*10¯) = 1.584 Nm /C
So total flux which is enclosed by the surface is = 1.584 Nm /C
Example 2:
If a wire of infinite length carries 0.4 C charge along every meter then electric field 0.3 m from
line charge is ?
From the application of Gauss law the electric field through line charge density is given by
formula:
E= λ/ 2Лrϵ₀
λ = Q/L = 0.4/1
E= 0.4/ 2Лϵ (0.3)₀
E= 2.4 * 10
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4. Permanent and electromagnets
Permanent magnets:
This type of magnet is capable of producing persistent magnetic field at its own due to
magnetised characteristics of its constituent material. Thus, its magnetic characteristics are
permanent and depends upon the material utilised for its fabrication. One of the disadvantage of
permanent magnet is that with time their strength is reduced and their poles are constant.
Permanent magnets produces magnetic fields at lower temperature thus it is not suitable for the
applications which are based upon high temperature (Weber and et.al., 2018). The magnetic
properties of permanent magnet can be regained or recovered only with the help of re-
magnetizing process. However contrary to the electromagnets it does not require regular
electrical supply to sustain its magnetic properties.
Electromagnets:
In electromagnets magnetic fields are produced by the electric current and thus its
strength can vary and depends upon the current flow (Krishnan, 2016). Electromagnets are made
up of coil which shows magnetic behaviour when current flows through it. Usually it is wrapped
with a ferromagnetic material so that its magnetic strength can be increased. This type of
materials are also able to hold and attract the ferrous materials.
Comparison:
One of the advantage of electromagnets is that they allow the controlled power handling.
Thus, the power can be released or hold as per the needs. It makes them highly suitable for the
applications based upon DC current. Both types of the discussed magnets possess magnetism
properties and have imaginary magnetic field lines. Though electromagnets have certain
advantages over permanent one such as variable magnetic strength and low cost but it also has
certain disadvantages. The key disadvantage of electromagnets is that continuous electric supply
leads to ohmic heating, core losses and voltage spikes which are not desirable. It is also observed
that as electromagnets require copper coupling in greater number so they cannot be used in small
space and is less feasible for maintaining and repairing in case of damage.
Applications:
Permanent magnets are used for converting electricity into mechanical forces, electric
motors, measuring instruments, trains, myriad applications, magnetic levitation and in generators
(Härtel, 2018). On the other hand electromagnets are primarily used in electrical transformers
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and other electric devices. The solar power applications and the machines which needs minimum
copper losses also employs permanent magnet. The versatility and strength of electromagnets
makes them suitable for industrial applications and in variety of electric devices such as lifting
magnets, relays, motors, data storage equipments, transformers loudspeakers and magnetic locks.
5. Bio- Savart law
Bio-Savart law is defined as the equation which describes the magnetic fields produced
due to a current carrying conductor or wire so that its strength can be determined at various
points. Thus, it describes the current as the source of magnetic field when the distance between
current source and field point is continuously changing (Greaves and et.al., 2018).
(Source:Biot-Savart Law, 2019)
This law states that in a current carrying wire magnetic field intensity (dH) at any point within
small length dl of wire is directly proportional to current (I), length element (dl) and sine θ where
θ is the angle between current direction and line joining dl and field point. It also states that dH is
inversely proportional to x where x is the distance between dl and point.
Mathematically,
dH α Idl Sin θ / x
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dH = k Idl Sin θ / x
Where,
k = [μ μr / 4Л]
dH = [μ μr / 4Л] xIdl Sin θ / x
is μr relative permeability of medium and
μ is absolute permeability which is = 4*10¯ Wb/A-m
Application:
Along with the key application of finding magnetic field this law is also efficient for
calculation of magnetic reactions at atomic or molecular level. Within aerodynamics this law is
also helpful for analysing the velocity (Punjala, 2016). It can calculate the magnetic field
strength due to electric field distribution in circular current carrying loop or in a finite straight
wire. The magnetic field at the centre of a current carrying loop is given by the expression: B=
μI/2r where I is the current flowing the loop and r is the radius.
Numerical example:
The Bio-Savart law can be used to solve the following problem:
Example:
If 5A current flows through a coil of radius 1 m then, find the magnetic field from a distance of
2m. Provided the number of turns in the coil are 10?
Solution:
Number of turns (n)= 10
I = 5A
l= 2m ; r = 1m
By applying Bio-Savart law
B = [μ/ 4Л] * (2ЛnI/r)
B = [μ/ 4Л] * (2Л * 10*5/1)
B= 314.16*10¯ T
6. Ampere force law
The force of attraction or repulsive between two current carrying wires is known as the
Ampere force law and is very important for determining magneto-static forces. The magnetic
field producing wire follows the Bio-Savart law while the other wire which experiences the field
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follows the Lorentz force law. Ampere force law describes the forces which occurs as a result of
motion of electric charges in the magnetic field (Ferreira, 2016). For the two wires carrying
current I1 and I2 respectively which are placed at a distance r, expression for the force per unit
length is as follows:
F/L = 2K*(I1*I2)/r
Where K is the constant of magnetic force and is equals to k = [μ μr / 4Л]
It is also possible that there may be significant difference between the lengths of wire.
One wire may have infinite length or they may have very small separation or the distance
between them.
Ampere force law can also be formulated in the form of line integral which also integrate
the Bio-Savart and Lorentz force law. This integral form of Ampere force law is:
F = [μ/ 4Л] ∫∫ [ I1.dl * (I2.dl * r)] / r
Where F is total force on first wire due to second wire.
Ampere force law is also considered as the analogue of Coulombs law. This law is seems
less applicable and effective under the influence of magnetizable substances. However, this law
provides one benefit that it gives clear definition of the ampere which is independent of any kind
of magnetic field. This law can be seldom used or applied for the practical engineering
applications and provides a foundation for defining the basic unit of electric current.
In the practical implementation the value of Ampere force is calculated deriving magnetic
field's value from the Bio-Savart equation and then that value is substituted in motor equation.
This law is valid only in free space and despite of being invalid in magnetizable materials it can
provide the magnetic flux density in terms of ampere (Zohuri, 2019). This law is based upon
current elements and practical realisation of isolated current elements is not possible within
electric circuits.
7. Toroisal coil
Toroisal coils or toroids is defined as the insulated wire which is wound on iron made
doughnut or circular shape structure. Solenoid are known as the structures which are made from
current carrying wires and acts as electromagnet. Solenoid are usually in helical shape in which
iron or other strong metallic substances are inserted. When solenoid is bent into a circular or
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doughnut shape it is known as the toroisal coil. The magnetic field inside this coil are in the form
of concentric circle while outside the coil magnetic field is equals to zero.
The strength of magnetic field depends upon the number of coils and is stronger in the
regions near inner part of ring. For the given number of turns, size and materiel toroisal coil has
more inductance as compare to the solenoid. This difference allows fabricating coils with high
inductance in low cost and smaller size.
Toroisal coils are made up of wires with large diameters so that the resistance is
decreased and more current can be conducted (Krishnan, 2016). Another difference which
distinguishes toroids with normal coils or solenoids is that as these coils does not have any
ending the magnetic flux is confined within core material and flux leakage problems does not
occur. It also prevents the interference from the external magnetic fields which can change or
affect the behaviour of coil. Thus, the use of toroisal coil protects the field interferences which
can change the other circuit components.
(Source: Magnetic Field of Toroid, 2019)
The superior electrical efficiency of toroidal based coils has lead to the replacement of
closed core transformers and inductors with the toroidal based inductors. The benefits of the
toroisal coil are due to its shape symmetry which voids magnetic flux leakage and
electromagnetic interference. The total magnetic field inside and outside the toroisal coil is zero
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Illustration 1: Toroisal coil

while the total magnetic field along circular turns has constant magnitude (Punjala, 2016). The
direction of this field is in clockwise direction and can be determined by the right hand thumb
rule. The expression for this magnetic field is given by:
B= μNI /Л /2r where
N = Number of turns
I is the current flowing through coil and r is the radius of toroisal coil
All wire loops which makes toroid produces magnetic field in the same direction within toroisal
coil. (Punjala, 2016)
Applications:
Toroisal coils have the property of self inductance and thus serve as an inductor. Due to
this reason they enhance the frequency level and stores energy as magnetic field. As compare to
the solenoids they are more economical and provides better enclosure of magnetic field. This
characteristic makes Toroisal coils suitable for the applications such as music instruments and
telecommunication. These coils are also very efficient in restricting or directing magnetic fields
so that the medical gears or the instrument working with resistance capacitor coupling can work
effectively.
RC motors performs their functions of communication, power feed with the help of these
coils. The electric motor can create troubles in the form of noise and voltage spike in flying
plane. Thus, to avoid this issue ferrite toroisal coils are added to electric motor so that plane can
fly without noise of functional errors. This coil finds its application in inverters, amplifiers,
power supplies and other electronic devices (Nousiainen and Koponen, 2017). Along with the
vast range of benefits toroisal coils also have some disadvantages. For instance these coils have
harder winding and thus they take longer time to tune. However, this drawback is compensated
by the high inductances.
CONCLUSION
It can be concluded from the above study electromagnetic devices find their usage in
wide range of practical applications. Thus, electromagnetic phenomenons and laws must be
evaluated and their application in practical equipments must be encouraged.
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REFERENCES
Books and Journals
Jiles, D., 2015. Introduction to magnetism and magnetic materials. CRC press.
Tran, M., 2018. Evidence for Maxwell’s equations, fields, force laws and alternative theories of
classical electrodynamics. European Journal of Physics, 39(6), p.063001.
Farrow, R., 2019. PHYS 121-102: Physics II.
Zohuri, B., 2019. Maxwell’s Equations—Generalization of Ampère-Maxwell’s Law. In Scalar
Wave Driven Energy Applications (pp. 123-176). Springer, Cham.
Greaves, A. and et.al., 2018. An electromagnetic and circuit theory concept inventory of
undergraduate engineering students. In 23rd AIP Congress and the Australian Optical
Society Conference 2018, Perth, Australia, 9-13 December 2018.
Krishnan, K.M., 2016. Fundamentals and applications of magnetic materials. Oxford University
Press.
Walecka, J.D., 2018. Introduction to electricity and magnetism. World Scientific Publishing
Company Pte Limited.
Chen, B., 2018, September. Research on the Application of Analogy Method in
Electromagnetism Teaching. In 2018 4th International Conference on Social Science and
Higher Education (ICSSHE 2018). Atlantis Press.
Nousiainen, M. and Koponen, I.T., 2017. Pre-Service Physics Teachers' Content Knowledge of
Electric and Magnetic Field Concepts: Conceptual Facets and Their Balance. European
Journal of Science and Mathematics Education, 5(1), pp.74-90.
Rothwell, E.J. and Cloud, M.J., 2018. Electromagnetics. CRC press.
Weber, N. and et.al., 2018. Electro-vortex flow simulation using coupled meshes. Computers &
Fluids, 168, pp.101-109.
Ferreira, S.F.S., 2016. Electromagnetic study of a variable inductor controlled by a DC
current (Master's thesis).
Härtel, H., 2018. Electromagnetic Induction from a new Perspective. European Journal of
Physics Education, 9(2), pp.29-36.
Punjala, S.S., 2016, March. Challenges in designing coils to enable wireless powering in electric
vehicles and their EMC safety compliance. In 2016 IEEE/ACES International
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Conference on Wireless Information Technology and Systems (ICWITS) and Applied
Computational Electromagnetics (ACES) (pp. 1-4). IEEE.
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