ElectromagnetismElectromagnetismLenz’s law and Maxwell’s equationsLenz’s law and Maxwell’s equations

By:Mahdi Dardashtian

As we all know, Electromagnetism is one of the four fundamental interactions of nature, along with strong interaction, weak interaction and gravitation. It is the force that causes the interaction between electrically charged particles; the areas in which this happens are called electromagnetic fields.

In our textbook, chapter 29, has concentrated on Electromagnetic Inductions and talks about Lenz’s law and Maxwell’s equations…

Have you ever heard of these two?

Does any body know how credit cards are working?

A credit card’s number, expiration date, and cardholder’s name are coded in a magnetized pattern in a strip on the back. When the card is “swiped” through a card reader, the moving stripe bathes the reader’s circuitry in a varying magnetic field that induces current into the circuit.

These currents transmit the information in the stripe to the cardholder’s bank.

What if card weren’t swiped, but just sat motionless in the reader’s spot?

This law has been introduced as 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 and current resulting from electromagnetic induction. H.E.F Lenz (1804-1865) was a Russian scientist who duplicated independently many of the discoveries of Faraday and Henry. Lenz’s law basically states that “…the direction of any magnetic induction effect is such as to oppose the cause of the effect.” This topic is just directly related to conservation of energy.

He put a definite direction to induced currents when the field was changing ( strictly when "Flux" is changing ). Faraday did not do this - his writings are rather confused on the matter. ( Yah can't be perfect all the time - remember - meters in the modern sense had not been invented!)

Lets look at this video…

As the magnet approaches the loop, the applied B field in the centre increases. This is a change.

An Induced Field is created which attempts to negate the applied field - ie to keep the total field at zero - its original value.

This Induced field must be associated with a current - the INDUCED CURRENT in the loop whose direction is determined by the first version of the right Hand rules - the one for predicting current - NOT the force one. Of course, the Induced EMF direction is clearly predicted by thinking of conventional currents flowing from positive to negative.

Lenz's Law is all about conservation of energy. It guarantees that induced currents get their energy from the effect creating the change. The force acting against the conductor being moved earlier is actually an invocation of Lenz's Law. ( As the conductor moves down, the flux increases, so the induced field opposes this which leads to the direction of the Induced current - which in turn shows the direction of the force back on the current.)

FIRSTLYWe are at a point to wrap up in a package

all of the relationships between electric and magnetic fields and their sources…

SECONDLYThis package consists of four equations,

called Maxwell’s equations…He didn’t discover them single-handedly

(though he developed the concept of the concept of displacement current)

He put them together and recognized their significance…

Who was he?...

James Clerk Maxwell (1831–1879) a Scottish theoretical physicist and mathematician who achieved to classical electromagnetic theory, synthesizing all previously unrelated observations, experiments and equations of electricity, magnetism and even optics into a consistent theory.

These four equations, together with the Lorentz force law are the complete set of laws of classical electromagnetism. The Lorentz force law itself was derived by Maxwell, under the name of Equation for Electromotive Force, and was one of an earlier set of eight equations by Maxwell.

Maxwell's equations are a set of four partial differential equations that relate the electric and magnetic fields to their sources, charge density and current density. These equations can be combined to show that light is an electromagnetic wave. Individually, the equations are known as Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction. The set of equations is named after him…

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.

…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.

The second is the analogous relation for magnetic field which states that the surface integral of B over any closed surface is always ZERO…

…where S is any closed surface (a "closed surface" is the boundary of some three-dimensional volume; the surface of a sphere or cube is a "closed surface", but a disk is not), dA is a vector, whose magnitude is the area of an infinitesimal piece of the surface S, and whose direction is the outward-pointing surface normal. The left-hand side of this equation is called the net flux of the magnetic field out of the surface, and Gauss's law for magnetism states that it is always zero.

It describes how a changing magnetic field can create (induce) an electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators…

E is the electric field,dℓ is an infinitesimal vector element

It states that magnetic fields can be generated in two ways: by electrical current (this was the original "Ampère's law") and by changing electric fields (this was "Maxwell's correction")

where is the closed line integral around the closed curve C;B is the magnetic field · is the vector dot product;dℓ is an element of the curve C (i.e. a vector with magnitude equal to the length of the infinitesimal line element, and direction given by the tangent to the curve C)μ0 is the magnetic constant;

Ienc is the net free current that penetrates through the surface S.

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