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# Electricity and Magnetism

There are many atoms around us which carry its fundamental particles. The fundamental particle electrons and protons carry negative and positive charges which are the reason for electricity. All particles carry the same charge but in opposite signs. The particles neutrons and protons are present in the nucleus while electrons are moved around the nucleus. The movement of electrons is the reason for electricity. We see electricity in the example lightning which is a spark or flash light.

Electricity dominates many parts of the world. Life without electricity would
be almost unrecognizable to many of us.

It is due to the movement of electrons. It can be formed unequal distribution of electrons. The flow of electricity also produces the magnetic field. This is the phenomena of electromagnetism which is used to form electromagnet. This is the force that exists between the charged particles. Here we are discussing the complete phenomena of electromagnetism and different types of magnetism.

## Electromagnetism

When electricity and magnetism are studied together, the effect of changing magnetic field is very important. Michael Faraday and Joseph Henry in the year 1831 independently proved that electromotive force gets induced in a closed circuit due to changing magnetic field. Electromotive force or current also gets induced when a closed loop of wire or conductor is moved under the influence of magnetic field. This forwards our discussion towards Faraday’s Law.

## Relationship Between Electricity and Magnetism

To understand the relation between the electricity and magnetism, we will discuss that how electromotive force gets induced due to the change in magnetic flux.

Faraday and Henry performed lots of experiments to learn about the connection between electricity and magnetism. The results of these experiments have led to the life styles of today's men, who made life easy by using lots of electrical applications.

Some of the experiments are as follows :

A solenoid is connected to a sensitive galvanometer. On moving a magnet towards a coil, the galvanometer shows a deflection. When the magnet is reversed, the deflection is seen to be in the opposite direction. Once the magnet is stopped, there is no deflection in galvanometer. On moving the magnet faster towards the coil, the deflection is longer.

Similar results are obtained when the magnet is kept stationary and the coil is moved. It means that whenever a current was induced in the coil there is a relative motion between the coil and the magnet. The magnitude of the current depended on the strength of the magnet and also on the magnitude of their relative velocity.

Similar results were seen when the magnet is replaced by as coil connected to a battery. Even without physically moving the coils a current was shown in the galvanometer only when the switch is on and when the current is put off i.e., when the current is building up in the coil or when it reduced to zero the galvanometer in the other coil showed a charge.

This current, which is produced in the coil connected to the galvanometer, is called as induced current. The induced currents direction, when the current builds up in the other coil was opposite to that when the current reduced opposite to that when the current reduced. The deflections were momentarily seen only when the switch was opened and closed. These observations can be summarized in Faraday's laws of electromagnetic induction.

Faraday's laws of electromagnetic induction:
1. Whenever the magnetic flux linked with a circuit changes, an EMF is induced in the circuit, which lasts as long as the change in magnetic flux associated with the circuit continues.
2. The magnitude of the induced EMF is equal to the rate at which the magnetic flux linked with the circuit changes.

Mathematically,

$\epsilon \propto$ $\frac {d\phi}{dt}$= $(\frac{\phi_{2}-\phi_{1}}{t})$ Where,$\frac {d\phi}{dt}$ is the rate of change in magnetic flux. This is the most important formula which states the relation between electricity and magnetism.

Faraday's laws of electromagnetic induction do not say anything about the direction of the current. The direction is given by Lenz's law.

## Electricity and Magnetism Equations

Main four formulas of Electricity and Magnetism are represented by Maxwell Equations. These four Formulas are Gauss Law, Gauss Law in Magnetism, Faraday’s Law and Amperes Maxwell Law. These formula’s are given below.

1) $\oint_{s} E.dA$= $\frac {Q}{\epsilon_{0}}$ ( Gauss's law )

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

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

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

## Electrical Theory

We know that every matter is composed of molecules and molecules are composed of atoms. The atoms have neutrons, electrons and protons as its constituent element. The electrons carry negative charge while protons carry positive charge and neutrons are neutral in nature. Using these definitions, the electric charge is the extent to which it contains electrons and protons.This section will help us to learn basic concepts of electricity, Voltage, Current, Resistance, Ohm's Law which connects them, and what Power means.

## Magnetism

Magnetism is a property associated with the materials which respond to the applied magnetic field. There are different electrical behaviors like ferromagnetism, Diamagnetism, Paramagnetism, antiferromagnetism.

Diamagnetism: It is stated as the property of the materials to oppose the external magnetic field applied to them. These materials are repelled when external magnetic field is applied to them. If we consider the electrical nature of the Diamagnetic material we will find that it does not have unpaired electrons because of which bulk effect is not produced by the magnetic moments of the electrons. In diamagnetic materials, magnetization is due to the orbital motion of the electrons.

Paramagnetism: These type of materials has unpaired electrons, that is they have one electron in the orbitals of atoms or molecules. As supported by the Pauli exclusion principle an unpaired electron in the paramagnetic materials can align their magnetic moment as they want. In any direction. When external magnetic field is applied to the Paramagnetic materials they tend to align in the direction of the applied magnetic field and reinforce the external magnetic field applied.

Ferromagnetism: Ferromagnetic materials also has unpaired electrons, similar to the Paramagnetic materials. As external magnetic field is applied to these materials, magnetic moment of the electrons align themselves to the applied electric field but in addition the magnetic moments of the electrons align themselves to each other. Because of this fact, even if we remove the applied field, the electrons maintain a parallel orientation to each other After the curie temperature the ferromagnetic materials lose their ferromagnetic properties, because of the disorder due to the high temperature. Examples are: cobalt, iron and nickel etc.

Antiferromagnetism: In Antiferromagnetic materials, corresponding to the magnetic moment of a single electron aligned in one direction there is another anti- aligned electron having magnetic moment in opposite direction . That is why Antiferromagnetic materials effective magnetic moment is zero. Examples of Antiferromagnetic materials is spin glass.

## Biot Savart Law

The Biot - Savart's law enables us to write the general results for the magnetic field due to an arbitrary current distribution or it is an experimental law predicted by Biot and Savart dealing with magnetic field strength at a point due to a small current element.

If AB represents a current element of a conductor PQ carrying current I and $\overrightarrow{r}$ the position vector of P from the current element AB (i.e., of length $\overrightarrow{dl}$), then the law states that magnetic field (dB) at P due to current element depends on

dB $\alpha$ I
dB $\alpha$ dl
dB $\alpha$ sin $\theta$ (angle between dl and r)
dB $\alpha$ $\frac{1}{r^{2}}$

Combining we get,

dB $\alpha$ $\frac{\mu_{0}}{4 \pi}$ $\frac{I dl sin\theta}{r^{2}}$
dB = $\frac{\mu_{0}}{4 \pi}$ $\frac{I dl sin\theta}{r^{2}}$
Where $\mu_{0}$ = 4 $\pi$ $\times$ 10-7 Tm/A

In Vector form, it can be represented as:

dB = $\frac{\mu_{0} I(\overrightarrow{dl} \times \overrightarrow{r})}{4 \pi r^{3}}$

The direction of dB is given by right Hand screw rule. The S.I unit is given by Tesla.

## Eddy Currents

When the conductor is exposed to the changing magnetic field, the changing magnetic field can cause the circulating flow of the electrons or the circulating flow of the current which flow within the body of the conductor.
A magnetic field is induced by these circulating current known as eddies which opposes the change of the original magnetic field and this is due to the Lenz's law and hence causing repulsive or drag forces between the conductor and the magnet.

Eddy currents which are also known as the Foucault currents are those currents which are induced in the conductors and which opposes the change in the flux being generated by these currents.

Example: When we heat a metal piece to red-hot state then the eddy currents become stronger. The magnitude of the eddy currents is dependent of the resistance of the metal. The magnitude of the eddy current is smaller for the larger values of resistance.

## Electromagnetic Induction

In 1831, the famous scientist Faraday discovered that whenever the number of magnetic lines of force or magnetic flux passing through the circuit changes, an emf is produced. If the circuit is closed, a current flows through it.
The emf and the current produced is called the induced emf and the induced current. This induced emf and the induced current lasts as long as the change in the magnetic flux continues. This phenomenon is called as the Electromagnetic induction.

## Lenz's law

The motion of the magnet in either direction causes a change in strength of the magnetic field linked with the coil and this causes a current to be induced in the coil. This induced current opposes the change in the magnetic field by producing its own magnetic field.

Below are given the following figure for Lenz's law:
Whenever an emf is induced, the induced current is in such a direction so as to oppose the change inducing the current.
$\therefore \varepsilon$ = - $\frac{d\phi}{dt}$The negative sign indicates the opposing nature of the induced EMF.

## Lorentz Law

It is evident from Faraday's law that whenever there is a change in the magnetic flux passing through a closed circuit, an electric current is induced in the circuit. It can be explained on the basis of Lorentz force.

A charge q moving with a velocity v in a magnetic field B, it experiences the magnetic force called the Lorentz force given by
F = q (v $\times$ B)The phenomena of motion emf can be explained through Lorentz force.

## Mutual Inductance

When current builds up or varies in a coil, the flux change leads to induced emf in the same coil. This is what we call Self induction.
Consider a coil which is undergoing self induction when current is passed through it. If another coil is brought near the first coil, the changes in the magnetic flux of the first coil produces similar changes in the second. Thereby, producing induced e.m.f in the second coil. This Phenomenon is called Mutual induction as the two coils are mutually interacting with each other.

Thus Mutual Induction is defined as:
It is the property of two circuits (or coils) by virtue of which each oppose any change in the magnitude of the current flowing through the other circuit by producing an induced EMF in it.