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EMF, EMI and Faraday’s Laws of EMI

(Needs edition and completion as per the video lectures in 6 parts)

EMF, EMI and Faraday’s Laws of EMI

Today we are going to talk about EMF, EMI and Faraday’s Laws of EMI

Broadly, Electromotive Force is the force that moves an electric charge. Such motion will generate a current. Discovery of current was as important for progress of human society as the discovery of Fire nearly thousands of years back or the construction of a steam engine by James Watt. Current electricity was the newest source of power that transformed the human life style.

Devices that can provide emf include voltaic cells, thermoelectric devices, and solar cells.

Another source of emf is the phenomenon of The electromagnetic induction which is used in electrical generators, transformers, and electrical motors.

Volta’s pile

Let us briefly see the historical context. In 1800, which is nearly 210 years back, Volta created the historic Voltaic pile by piling up several pairs of alternating copper and zinc discs which he called electrodes separated by cloth soaked in brine which serves as electrolyte conductor and increases the conductivity inside the pile. He then connected the top and bottom discs by a wire, and an electric current flowed through the wire.

The strength of the pile is expressed as its electromotive force, or emf, its unit being volts – u guessed correctly, this unit is named after Volta. He was able to measure the characteristic emf of different pairs of metals. Now the phenomenon is understood more precisely, the electric potential difference is created because of separation of positive and negative charges as a result of electrode-electrolyte reaction.

The emf is therefore defined as the external work done per unit of charge to produce an electric potential difference across two open-circuited terminals. Thus ℰ = dW/dq

The created electrical potential difference drives current flow if a circuit is attached to the source of emf. When current flows, however, the voltage across the terminals of the source of emf is no longer the open-circuit value, due to some voltage drops inside the device due to its internal resistance.

In the voltaic piles or their refined mode, namely battery, chemical reactions at the electrodes results in charge separation that further gives rise to a voltage difference.

The emf will move positive charge from a point of low potential through its interior to a point of high potential. And in the process, performs work dW on that charge to move it to the high potential terminal.

The reactions at the electrode–electrolyte interfaces provide the emf for the voltaic cell, In the open-circuit case, charge separation continues until the electrical field from the separated charges is sufficient to arrest the reactions, this is why an open circuit battery will not drain out early. That is why it is recommended to open the battery in cars when the car is not likely to be used for a long time.

• The overall electrochemical cell reaction can be written as 2 half-equations:
      1 equation for the reduction reaction (electron are gained) and 1 equation for the oxidation reaction

• The number of electrons gained in the reduction half reaction must equal the number of electrons lost in the oxidation half reaction

• The cell's emf is calculated by adding together the E values for each half reaction:
      E_cell = E_reduction + E_oxidation

• If the concentration of reactants increases relative to products, the cell reaction becomes more spontaneous and the emf increases.
      As the cell operates, the reactants are used up causing the emf to decrease.

K⁺+e  K(s) -2.92

Al³⁺+3e  Al(s) -1.66

Zn²⁺+2e  Zn(s) - 0.76

Ni²⁺+2e  Ni(s) - 0.23

Cu⁺+e  Cu(s) 0.52

Ag⁺+e  Ag(s) 0.80

A solar cell or photodiode is another source of emf, with light energy as the external power source.

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EMI

The electromagnetic induction was discovered by Faraday in1831 and this itself was based on the earlier work of Oersted. Henry and later Maxwell are other 2 scientsts who also worked on the concept

EMI is the production of voltage across a conductor moving through a magnetic field.

The Faraday’s Laws of EMI states that:

The induced electromotive force (emf) in any closed circuit is equal to the rate of change of the magnetic flux through the circuit and in a direction that opposes the change in flux.

In practice, this means that an electric 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. Thus

where

  is the electromotive force (emf) in volts

is the magnetic flux in webers per loop

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

where

N is the number of turns of wire

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 is the reason of the minus sign in the above equation

If the rate of change of current in a circuit is one ampere per second and the resulting electromotive force is one volt, then the inductance of the circuit is one henry.

Always think in terms of the pair Effort and flow. Their product is power.

when effort is FORCE then flow is velocity and FxV = power

when effort is EMF the flow is current and VxI = power

If Magnetic field is B, and length of conductor is l, and a current I is passed, then

Conductor will experience a force =Bil and if velocity is v then power = Fv=Bilv

The emf generated across the conductor is E = Blv. Power = emf x current = Blvi

Formal definitions of electromotive force

Inside a source of emf that is open-circuited, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf. Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition (the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit).^[22] Mathematically:

where E_cs is the electrostatic field created by the charge separation associated with the emf, dℓ is an element of the path from terminal A to terminal B. This equation applies only to locations A and B that are terminals, and does not apply to paths between points A and B with portions outside the source of emf.

In the case of a closed path in the presence of a varying magnetic field, the integral of the electric field around a closed loop may be nonzero; one common application of the concept of emf, known as "induced emf" is the voltage induced in a such a loop.^[24] The "induced emf" around a stationary closed path C is:

where now E is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary but stationary closed curve C through which there is a varying magnetic field. Note that the electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative (that is, the work done against the field around a closed path is zero).

This definition can be extended to arbitrary sources of emf and moving paths C:^[25]

which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.

Magnetic Flux inside a coil --

In the case of an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which in turn creates an energy difference between generator terminals. Charge separation takes place within the generator, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further movement unfavorable. Again the emf is countered by the electrical voltage due to charge separation. If a load is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines is Faraday's disk

Faraday's law of induction.

In Faraday's first experimental demonstration of electromagnetic induction (August 1831), he wrapped two wires around opposite sides of an iron torus (an arrangement similar to a modern transformer). Based on his assessment of recently-discovered properties of electromagnets, he expected that when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire to a battery. Indeed, he saw a transient current (which he called a "wave of electricity") when he connected the wire to the battery, and another when he disconnected it. Within two months, Faraday had found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near a bar magnet with a sliding electrical lead ("Faraday's disk").

Faraday explained electromagnetic induction using a concept he called lines of force.

Lenz's law is a common way of understanding how electromagnetic circuits must always obey Newton's third law. Lenz's law says:

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

Connect the terminals of a weak cell to a

galvanometer. Observe the deflections of the

needle. Remove the cell and connect a

solenoid to a galvanometer. Observe the

deflections of the needle by continuously

moving a magnet into and out of the solenoid

(fig 3.1b).

The needle deflects only in one direction

when the galvanometer is connected to a cell.

Thus a current flowing only in one

direction is called direct current (DC).

The needle is seen deflecting to either

side when the galvanometer is connected to

the solenoid in the above experiment.

The direction of the electric current

produced by the movement of the magnet in

opposite directions continuously changes. Thus

the current which changes its direction at

regular intervals is called alternating current.

(AC).

AC generator (Alternator)

The device which produces electricity on

the basis of electromagnetic induction by the

continuous motion of either the solenoid or the

magnet is called a generator.

Let us see the working of a model AC generator.

parts of the generator

􀁺 Armature

Field magnet

Slip

rings

Brush

An armature is an arrangement of an

insulated conducting wire wound around a soft

iron piece. The armature is continuously

rotated by means of mechanical energy. Figure

3.3 shows the different stages of the rotation

of the armature between the pole ends of the

field magnet. Find out answers to the

questions given below by analysing the graph

along with the figure (3.3).

􀁺 There is no electricity in the armature coil

at the stages 1,3 & 5.Why?

􀁺 Why is the electricity obtained at the

stages 2 & 4 the maximum?

􀁺 What is the reason for the different

directions of the current in stages 2 and

4?

􀁺 What are the angles of the rotation at

which the emf in the armature is

maximum?

􀁺 How do the direction and the magnitude

of the emf change during one rotation of

the armature?

Let us see how the electric current from a

DC generator flows in one direction in the

external circuit.

The positions of the two half rotations of

the armature in a DC generator are given in

the figure (fig 3.6)

Here the AC induced in the armature is

converted into DC in the external circuit by

an arrangement called split ring commutator.

The flux cut in the first half of the rotation is in

one direction and in the opposite direction

during the second half rotation. Hence the

direction of flow of current in the armature

changes. When the direction of the current in

the armature changes during the successive

half rotations, the conatct of one half of the

split ring shifts from one brush to the other.

So the direction of the current in the external

circuit does not change.

An armature is an arrangement of an

insulated conducting wire wound around a soft

iron piece. The armature is continuously

rotated by means of mechanical energy. Figure

3.3 shows the different stages of the rotation

of the armature between the pole ends of the

field magnet.

Electromagnetism

On 21 April 1820, during a lecture, Ørsted noticed a compass needle deflected when an electric current from a battery was switched on and off, confirming a direct relationship between electricity and magnetism. His initial interpretation was that magnetic effects radiate from all sides of a wire carrying an electric current, as do light and heat. Three months later he published his findings, showing that an electric current produces a circular magnetic field as it flows through a wire. This discovery was not due to mere chance, since Ørsted had been looking for a relation between electricity and magnetism for several years. The special symmetry of the phenomenon was possibly one of the difficulties that retarded the discovery.

3.09 Mutual induction

An insulated copper wire is wound

around one end of a soft iron core and the

ends of the coil are connected to a battery

through a switch. Another insulated copper

wire is wound around the other end of the

core. Connect the ends of this coil to a

galvanometer. Of these, the circuit which is

connected to the battery is called primary

circuit and that connected to the galvanometer

is called secondary circuit. Note down the

deflections in the galvanometer when the

primary circuit is switched on or off.

Why does the galvanometer needle

deflect? That is because an emf is produced

in the secondary. Then how is it produced?

Is this the emf of the cell?

When there are two nearby coils the

variation of current in one of them produces a

change in the magnetic flux around it. The

second coil is situated in this region of varying

magnetic flux. Therefore by electromagnetic

induction an emf is induced in the secondary

coil. This phenomenon is called mutual

induction.

Self induction is the phenomenon of

inducing an emf in a coil caused by the

variations of magnetic flux produced by a

varying current in the same coil.

3.11 Transformer

Arrange two insulated solenoids over a

soft iron core as shown in figure 3.13. (both

must have almost the same number of turns).

Maxwell's equations 1861. are a set of four partial differential equations describing how the electric and magnetic fields relate to their sources, charge density and current density, and how they develop with time.

Thus, these equations are of basic importance for the totality of physical and electrotechnical phenoma, concerning the fields of classical electrodynamics, classical optics, and the present radio-, television-, phone-, and information-technologies.

The equations are named after the Scottish physicist and mathematician James Clerk Maxwell who first published the equations known as Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.

Often, two equations for the electromagnetic field tensor that give an equivalent relativistic formulation are also called the Maxwell equations. Furthermore, there is also a formulation with one differential two-form and its dual.

The four equations, together with the Lorentz force law completely describe 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. As mentioned, the equations are fundamental to physics and engineering alike. The main reason is that the equations show the existence of electromagnetic waves, propagating in vacuum and in matter. Seemingly different phenomena like radio waves, visible light, and X-rays are then understood, by interpreting them all as propagating electromagnetic waves with different frequency.

The Maxwell equations have also been the starting point for the development of relativity theory by Albert Einstein because they predict the existence of a fixed speed of light, independent of the speed of the observer.

• Gauss' law 1835, describes how an electric field is generated by electric charges: The electric field tends to point away from positive charges and towards negative charges. More technically, it relates the electric flux through any hypothetical closed "Gaussian surface" to the electric charge within the surface.

• 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.

• Gauss' law for magnetism states that there are no "magnetic charges" (also called magnetic monopoles), analogous to electric charges.^[1] Instead the magnetic field is generated by a configuration called a dipole, which has no magnetic charge but resembles a positive and negative charge inseparably bound together. Equivalent technical statements are that the total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.

• In classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère in 1826,^[1] relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it again electrodynamically which form the basis of classical electromagnetism.

• An electric current produces a magnetic field.

Some physicists have remarked that Faraday's law is a single equation describing two different phenomena: The motional EMF generated by a magnetic force on a moving wire, and the transformer EMF generated by an electric force due to a changing magnetic field.