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Electricity and Magnetism

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Electricity is a form of energy, associated with electric charge and atomic particles such as electrons and protons. Electricity is both a basic part of nature and one of our most widely used forms of energy. Electricity occurs when electric charge flows between protons and electrons. 
Magnetism is a property associated with the materials which respond to the applied magnetic field. There are different electrical behaviors like Ferromagnetism, Diamagnetism, Paramagnetism, and Antiferromagnetism.

Electromagnetism

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Electricity and magnetism are two aspects of electromagnetism. Electric forces are produced by electric charges either at rest or in motion. Magnetic forces, on the other hand, are produced only by moving charges and act solely on charges in motion. Electric and magnetic forces can be detected in regions called electric and magnetic fields. Electricity and Magnetism that gives us another form of magnetism called Electromagnetism.
Hans C Oersted's discovered that magnetic fields can be produced using electric currents while Michael Faraday showed that a changing magnetic field can produce a induced current in a circuit and even James Clerk Maxwell predicted that a changing electric field has a magnetic field associated with it using electromagnetic waves. Thus there came a common point that electricity and magnetism are related concepts.

Magnetism    

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Magnetism is the phenomenon associated with the motion of electric charges. It is a force of attraction or repulsion between various substances, especially those made of iron, cobalt and certain other metals; ultimately it is due to the motion of electric charges. One end of the magnet is called a north pole and the other end a south pole. The force between a north and a south pole is attractive, whereas the force between like poles is repulsive. 
Magnetism is a force of attraction or repulsion that acts at a distance. It is due to a magnetic field, which is caused by moving electrically charged particles. It is also inherent in magnetic objects such as a magnet. The magnetic field of an object can create a magnetic force on other objects with magnetic fields. That force is what we call magnetism. There are four types of magnetism shown by the materials namely,
1) Ferromagnetism
2) Diamagnetism
3) Paramagnetism 
4) Antiferromagnetism

Ferromagnetism is that observed in iron, nickel and other materials. These materials once magnetized retain its property even after the field is removed. Magnetism produces forces large enough to be easily felt, and ferromagnetic materials are the only ones that demonstrate spontaneous magnetism.
Diamagnetism is that what causes repulsive force in materials when magnetic field is removed. This is observed in materials like alcohol, water, air etc. Diamagnetic materials such as pyrolytic carbon and mercury create a repulsive force.
 Paramagnetism is that where materials like aluminum, platinum undergoes magnetism when field is applied but loose the magnetization as soon as field is removed. Paramagnetic materials such as tungsten and aluminum create an attractive force when exposed to magnetic fields
Antiferromagnetism - Antiferromagnetic solids exhibit special behavior in an external magnetic field, depending on the temperature. At temperatures below Néel temperature, an antiferromagnetic material displays no magnetism. Antiferromagnetic materials are relatively uncommon - most are transition metal compounds, usually oxides (nickel oxide).

Electrical theory is based on theory of atomic structure. An atom consists of central nucleus having positively charged protons surrounded by negatively charged electrons in motion. This motion of electrons causes current known as electric current. The electrical theory is all about it.
Atomic Structure
Electrical theory gives us idea about concepts related to electricity like voltage, current, resistance, power. It is  due to flow of electrons. There are many things to be studied like how current flows, components and devices used for the flow, nature of the flow etc. A potential difference across the conductor lead to flow of electrical charge. This flow gives out the electrical current. The electrical current is the charge transferred per unit time.
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Electricity and Magnetism Equations

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The electricity and magnetism has many equations to be studied. The known equations are Maxwell's equations given below:
$\oint_{s} E.dA$ = $\frac {Q}{\epsilon_{0}}$ ( Gauss's law )

$\oint_{s} B.dA$ = 0 ( Gauss's law in magnetism )

$\oint E.ds$ = - $\frac {d\phi_{B}}{dt}$ ( Faraday's law )

$\oint B.ds$ = $\mu_{0} I + \epsilon _{0}\mu _{0}$ $\frac {d\phi_{E}}{dt}$ ( Ampere-Maxwell law )

Electromagnetic Units

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There are many units in electricity and magnetism. Here are given some electromagnetic terms and their units:
  1. Electric current in Amperes (A)
  2. Electric charge in coulomb (C)
  3. Potential difference Volts (V)
  4. Electrical resistance ($\Omega$)
  5. Resistivity ($\Omega$ meter)
  6. Electric power in watts (W)
  7. Capacitance in Farad (F)
  8. Electric flux in Volt metre (Vm)
  9. Electric field strength in volt per metre (V/m)
  10. Electric displacement field in Coulomb per square meter (C/m2)
  11. Permittivity in farad per meters (F/m)
  12. Conductance ($\Omega^{-1}$)
  13. Magnetic flux (Wb)
  14. Magnetic field strength A/m (Am-1)
  15. Inductance in Henry (H)
  16. Permeability in Henry per meter (Hm-1).

Relationship between Electricity and Magnetism

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Electricity and magnetism are interrelated concepts. The changing magnetic field gives the electrical current whereas the changing electric field gives out magnetic field.  It tells about how electromotive force gets induced due to the changing magnetic flux.

Electricity and magnetism are two aspects of the same force. Electricity and Magnetism that gives us another form of magnetism called Electromagnetism. A changing magnetic field induces electrical current in a wire, and is the basis for electrical generation. You can't have electricity without magnetism and vice versa.  

Electromagnetic Induction

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Whenever an electric current flows through a conductor, a magnetic field is immediately brought into existence in the space surrounding the conductor. This phenomenon whereby an emf and current is induced in any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic induction.
Electromagnetic Induction was first discovered way back in the 1830’s by Michael Faraday. Faraday noticed that when he moved a permanent magnet in and out of a coil or a single loop of wire it induced an Electromotive Force or emf, in other words a Voltage, and therefore a current was produced. It was a way of producing an electrical current in a circuit by using only the force of a magnetic field and not batteries. This then lead to a very important law linking electricity with magnetism, Faraday’s Law of Electromagnetic Induction.

Eddy Currents

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Eddy Currents are closed loops of induced current circulating in planes perpendicular to the magnetic flux. They normally travel parallel to the coil's winding and the flow is limited to the area of the inducing magnetic field. Eddy Currents near the surface can be viewed as shielding the coil's magnetic field, thereby weakening the magnetic field at greater depths and reducing induced currents. In conductors the electrons swirl in a plane perpendicular to magnetic field. It produces the repulsive force between conductor and magnet.
Eddy Current

Faraday Law

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Faraday's law of induction is a basic law of electromagnetism. This law shows the relationship between electric circuit and magnetic field. This law explains the working principle of most of the electrical motors, generators, electrical transformers and inductors.

Faraday First Law states that any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. Methods to change magnetic field are: by moving a magnet towards or away from the coil, by moving the coil into or out of the magnetic field, by changing the area of a coil placed in the magnetic field, by rotating the coil relative to the magnet.

Faraday's Second Law states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.

It is given as
$\epsilon$ $\propto$ $\frac{d \phi}{dt}$ = $\frac{\phi_2 - \phi_1}{t}$
Here $\frac{d \phi}{dt}$ is the change in magnetic flux.

Biot Savart Law

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Biot-Savart law, in physics, a fundamental quantitative relationship between an electric current and the magnetic field it produces, based on the experiments in 1820 of the French scientists Jean-Baptiste Biot and Félix Savart. It is the mathematical way to find the magnetic field at any point from a distance of a current carrier.
Magnetic Field Current Element
If AB is a current carrying element of a conductor PQ carrying current I and $\vec{r}$ the law tells that the magnetic field dB at P is given by
dB = $\frac{\mu_o}{4 \pi}$ $\frac{I dl sin \theta}{r^2}$Biot savart's law tells how magnetic field relates to currents. It states that current carrying element dB is directly proportional to the current I and the length l of the current element and inversely proportional to the cube of the distance d between the element and point where magnetic field is determined. The S.I unit is given in tesla.

Lenz's Law

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Lenz's law is named after the German scientist H. F. E. Lenz in 1834. Lenz's law states that when an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such, that it produces an electric current that's magnetic field opposes the change which produces it.
Faraday Law Formula
Where
e = Induced emf
dFB = change in magnetic flux
N = No of turns in coil
t is the time taken

Lorentz Law

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After the Dutch physicist Hendrik A. Lorentz, the Lorentz Force Law can be used to describe the effects of a charged particle moving in a constant magnetic field. The simplest form of this law is given by the scalar equation. Lorentz force, the force exerted on a charged particle q moving with velocity v through an electric E and magnetic field B. The entire electromagnetic force F on the charged particle is called the Lorentz force and is given by
Lorentz Law
Assume a charge q is moves with velocity v in a magnetic field B the Lorentz force is
Lorentz Force Formula
Here F is the force
E is electric field
B is magnetic field
q is electric charge
v is the velocity at that instant.

Induction Heating

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Induction heating works on the basic principles of electricity. When an alternating electrical current is applied to the primary of the transformer an alternating magnetic field is created. If the secondary of the transformer is located within the magnetic field, an electric current will be induced. Induction heating is a process which is used to bond, harden or soften metals or other conductive materials. With induction heating, heat is actually "induced" within the part itself by circulating electrical currents. Induction heating relies on the unique characteristics of radio frequency (RF) energy.

Induction Heating
Here we get induced electric current within the magnetic field.