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THE LAWS OF PHISYCS AND THEEXPLANATIONS

Introduction

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In its purest sense, physics is the study of the way matter and energy interact in

nature. Since early civilization, humans have sought to describe the workings of the

world around them. Physics attempts to predict the outcome of an event by

knowing certain conditions beforehand. For example, physics can predict how long

it will take for a rock to fall down a well, or how fast a pendulum will swing.

Coulomb’s law

Coulomb's law is a law of physics describing the electrostatic interaction between

electrically charged particles. It was studied and first published in 1783 by French

physicist Charles Augustin de Coulomb and was essential to the development of 

the theory of electromagnetism. Nevertheless, the dependence of the electric force

with distance (inverse square law) had been proposed previously by Joseph 

Priestley and the dependence with both distance and charge had been discovered,

but not published, by Henry Cavendish, prior

to Coulomb's works. 

Limitations of coulomb’s law

Coulomb's law has two major

limitations

[a] It is valid for charges at rest only: As the

coulomb's law measures the force of 

interaction between the charges thus if the

charges are moving then in addition to the Coulombic force another magnetic force

comes into play and net force is the vector sum of force due to Coulombic

interaction and the magnetic force.

[b] It is valid for point charges only: If the charges have some appreciable

dimensions then the charge on one body will vary the charge distribution in the

other body, thus the effective distance between the charges will not be distance

between their center of mass. Due to change in distance the force will also vary

Gauss’s law of electricity

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In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating

the distribution of electric charge to the resulting electric field. Gauss's law states

that: 

“The electric flux through any closed surface is proportional to the

enclosed electric charge.”

 The law was formulated by Carl Friedrich Gauss in 1835, but was not published until

1867.[1] It is one of the four Maxwell's equations, which form the basis of classical 

electrodynamics. Gauss's law can be used to derive Coulomb's law and vice versa.

Explanation

Gauss's law may be expressed in its integral form:

Where the left-hand side of the equation is

a surface integral denoting the electric flux through

a closed surface S, and the right-hand side of the

equation is the total charge enclosed by S divided

by the electric constant.

Gauss's law also has a differential form:

Where ∇ · E is the divergence of the electric field, and ρ is the charge density.

 The integral and differential forms are related by the divergence theorem, also

called Gauss's theorem. Each of these forms can also be expressed two ways: In

terms of a relation between the electric field E and the total electric charge, or in

terms of the electric displacement field D and the free electric charge .Gauss's law has a close mathematical similarity with a number of laws in other

areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity. In

fact, any "inverse-square law" can be formulated in a way similar to Gauss's law:

For example, Gauss's law itself is essentially equivalent to the inverse-

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the wire. In this case, the magnetic field-strength is the same at all points on theloop. In fact,

(3)

Moreover, the field is everywhere parallel to the line elements which make up theloop. Thus,

(4)

Or

(5)

In other words, the line integral of the magnetic field around some circular loop ,centered on a current carrying wire, and in the plane perpendicular to the wire, is

equal to times the current flowing in the wire. Note that this answer is

independent of the radius of the loop: i.e., the same result is obtained by takingthe line integral around any circular loop centered on the wire.

In 1826, Ampère demonstrated that Eq. (5) holds for any closed loop which circlesaround any distribution of currents. Thus, Ampère's circuital law can be written:

The line integral of the magnetic field around some closed loop is equal to thetimes the algebraic sum of the currents which pass through the loop.

In forming the algebraic sum of the currents passing through the loop, thosecurrents which the loop circles in an anti-clockwise direction (looking against thedirection of the current) count as positive currents, whereas those which the loopcircles in a clockwise direction (looking against the direction of the current) count asnegative currents.

Ampère's circuital law is to magnetostatics (the study of the magnetic fieldsgenerated by steady currents) what Gauss' law is to electrostatics (the study of theelectric fields generated by stationary charges). Like Gauss' law, Ampère's circuital

law is particularly useful in situations which possess a high degree of symmetry.

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Faradays law of electromagnetic induction

Electromagnetic induction is the production of  voltage across a conductor  situated

in a changing magnetic field or a conductor moving through a stationary magnetic

field.

Michael Faraday is generally credited with the discovery of the induction

phenomenon in 1831 though it may have been anticipated by the work of Francesco 

Zantedeschi in 1829. Around 1830 to 1832  Joseph Henry made a similar discovery, but

did not publish his findings until later.

Explanation

Faraday found that the electromotive force (EMF)

produced around a closed path is proportional to the rate

of change of the magnetic flux through

any surface bounded by that path. 

In practice, this means that an electrical current will be

induced in any closed circuit when the magnetic flux

through a surface bounded by the conductor changes.

This applies whether the field itself changes in strength or the conductor is moved through it.

Electromagnetic induction underlies the operation of generators, all electric

otors, transformers, induction motors, synchronous motors, solenoids, and most

other electrical machines.

Faraday's law of electromagnetic induction states that:

Thus:

Is the electromotive force (emf) in volts

ΦB is the magnetic flux in webers

For the common but special case of a coil of wire, composed of N loops with the same

area, Faraday's law of electromagnetic induction states that

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Where

Is the electromotive force (emf) in volts?

N is the number of turns of wire

ΦB is the magnetic flux in webers through a single loop.

A corollary of Faraday's Law, together with Ampere's and Ohm's laws is Lenz's law:

The emf induced in an electric circuit always acts in such a direction that the current it drives around the circuit

opposes the change in magnetic flux which produces the emf.

The direction mentioned in Lenz's law can be thought of as the result of the minus sign in the aboveequation

Lenz’s law

Lenz's law (pronounced /ˈlɛntsɨz

ˌlɔː/) is an extension of the law

of conservation of energy to the

non-conservative forces

in electromagnetic induction. It

can be used to give the direction of 

the induced electromotive

force (emf) and current resulting

from electromagnetic

induction. Heinrich Lenz postulated the following law;

"An induced current is always in such a direction as to oppose the motion or change

causing it"

 The law provides a physical interpretation of the choice of sign in Faraday's law of  

induction, indicating that the induced emf and the change in flux have opposite

signs.

Explanation of Lenz’s law

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Lenz's Law states that in a given circuit with an induced EMF caused by a change in

a magnetic flux, the induced EMF causes a current to flow in the direction that

opposes the change in flux. That is, if a decreasing magnetic flux induces an EMF,

the resulting current will oppose a further decrease in magnetic flux. Likewise, for

an EMF induced by an increasing magnetic flux, the resulting current flows in a

direction that opposes a further increase in magnetic flux.It is important to note that the induced current will always flow in a direction which

opposes any change of magnetic flux, but it does not oppose the magnetic flux

itself. If a magnet moves towards a closed loop, then the induced current in the loop

creates a field that exerts a force opposing the motion of the magnet. The current

loop creates a magnetic field similar to that of a magnet with its North Pole pointing

towards the north pole of the magnet. Then the south pole of the induced magnetic

field would be in the direction of the north pole of the magnet, to which the magnet

would be accelerated by the field. As the magnet accelerates, the current in the

loop would increase, causing an increasing force on the magnet and an increasing

acceleration.

References

David Halliday, Robert Resnick. New age international publishers.

 Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity,

Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman

Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice

Hall.

Heinz E Knoepfel (2000). Magnetic Fields: A comprehensive theoretical treatise for 

 practical use. Wiley.

George E. Owen (2003). Electromagnetic Theory (Reprint of 1963 ed.). Courier-Dover Publications.

J.C. Slater and N.H. Frank (1969). Electromagnetism (Reprint of 1947 ed.). Courier 

Dover Publications.

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