the laws of phisycs and the explanations
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Assignment On
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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