Electromagnetic Devices

Electromagnetic Devices

Table of Contents
1 Scalar and vector fields.................................................................................................................1
2 Coulomb's law...............................................................................................................................3
3 Gauss law......................................................................................................................................5
4. PERMANENT MAGNET AND ELECTROMAGNET.............................................................8
5. BIOT-SAVART LAW...............................................................................................................11
6. AMPERE'S FORCE LAW........................................................................................................14
7. TOROIDAL COIL.....................................................................................................................16
REFERENCES..............................................................................................................................20

1 SCALAR AND VECTOR FIELDS
Scalar field refers to a quantity which has only magnitude. No direction is defined to
scalar quantities. Scalar fields are addressed to be independent of coordinate system and same
units will be observed from every direction. It also describes potential energy of physical
quantities defined with a specific force. Examples of scalar field which is used are temperature,
pressure, higgs field. Scalar field is applied to many theories in physics which are illustrated
below:
· A scalar field combined with spin-0 particles in quantum field theory. Charged particles
are represented by scalar fields which is complex.
· Scalar field is used to solve horizon problem. These are supposed to cause accelerated
expansion of universe.
· Scalar field is used to illustrate gravitation field.
Vector field refers to a quantity which has moth magnitude and direction. It is dependent
on coordinate system and can be represented by arrows which shows both magnitude and
direction along with quantity.
A force is represented as a vector quantity because a force is applied in a specific direction. It
can be changed from one point to another point. Example of vector field are illustrated below:
· Air movements can be represented with vector field on earth wind has both speed and
direction and can be visualised with an arrow.
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· A fluid which is moving is visualised as a vector quantity because it is associated with
velocity that is a vector quantity.
Difference between scalar and vector fields are described below:
Scalar field Vector field
It has only magnitude. It has both magnitude and direction.
It is one dimensional quantity. It is multidimensional quantity.
It has simple comparison between two
quantities.
It has complex comparison between two
quantities.
Operations can be performed easily in scalar
representation.
Operations can not be performed in vector
quantities.
Vector fields are most complex one. Direction is represented by an arrow (Cooray,
Rachidi and Rubinstein, 2017). In case of 3-D dimension, three unit vector are noted:
· î is represented as unit vector in x- direction.
· Ĵ is represented as unit vector in y- direction.
· K is represented as unit vector in z- direction.
Length of arrow above quantity do not represent the size or length. It is a general representation
of vector quantities.
Lets explain scalar and vector field by taking an example:
· a player who is playing football is running 20 miles per hour from starting to end. Is it
scalar or vector?
Solution: this is a vector field because it has magnitude of 20miles per hour and direction
is given from starting to ending.
· Temperature of room is observed to be 35 degree Celsius. Is it scalar or vector?
Solution: this is a scalar because it has only magnitude. Temperature do not have
direction.
· A force which is applied on a body which is shown by a point on Cartesian plane and it
has coordinates as (3,4). how can it is represented as vector form?
Solution: a point (3,4)can be represented as f(x,y) = 3î + 4Ĵ .
in this î and Ĵ are vector units which shows direction in x-plane and y- plane
respectively.
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2 COULOMB'S LAW
Coulomb's law is a law of physics which quantifies the amount of force either between
two stationary or electrically charged particles. A electrostatic force between two charged
electrical bodies is called coulomb force. It is very important in theory of electromagnetism to
discuss quantity of electric charge. It generally gives an idea about force between two point
charges.
Therefore, Coulomb law states that “magnitude of electrostatic force of attraction or
force of repulsion between two charge points is directly proportional to product of magnitude of
charges and inversely proportional to distance between two point charges”.
Force of attraction or repulsion on the basis of above statement can be represented as
F q1*q2∝
F 1/ r∝ 
F q1*q2/r∝ 
hence it can be formulated as to calculate force of attraction or repulsion is
F = k q1*q2/r
here, F = force of attraction
q1, q2 = quantity of charge points
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r = distance between two charge points
k = proportionality constant = ¼ π ε₀ = 8.987551787 * 10 N. m .C ̃  
There are three conditions which needs to be assessed while considering coulomb's law:
· charge should have spherical distribution symmetrically. It can be either point charges or
charged metal sphere.
· Overlapping of charges should not be there.
· Charges must be stationary with respect to each other.
According to this law, charges with opposite signs attract each other and charges with same sign
repel each other. Size of charges is small as compared to distance between toe charges. Therefore
size of charge is approximated as negligible (Halliday, Resnick and Walker, 2016). SI unit of
electrostatic force is newton, distance is in metre and charges is in coulomb.
Let's take examples to calculate coulomb force between two point charges.
· Two charges of value 1C and -9C are kept at a distance of 9m. Find coulomb force and
show that it is attraction force or repulsion force.
Solution : coulomb force can be calculated by formulae F = k q1*q2/r
here, F = 9*10 * 1*9/ 9 
F = 10 newton.
As charges are of opposite sign,
it represents that it is an electrostatic force of attraction.
· Two point charges has a value of +3.37 μC and -8.21 μC. Force of attraction is given as
0.0626 newton. Find the distance between two point charges.
Solution: coulomb force can be calculated by formulae F = k q1*q2/r but here, distance needs to
be calculated. So, by putting values in above formulae:
0.0626 = 9*10 * 3.37* 8.21/ r 
= r = 9*10 * 3.37* 8.21/ 0.0626 
= r = sqrt (3.98)
= r = 1.99 m
Coulomb's law to find electrostatic force can be compared with gravitational force
because their point charges are replaced by mass of body. Distance between bodies or charges is
inversely proportional to gravitational force or electrostatic force respectively.
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