EMF, EMI and Faraday’s Laws of EMI

EMF, EMI and Faraday’s Laws of EMI
EMF, EMI and Faraday’s Laws of EMI
Today we are going to learn about EMF, that is Electro motive Force, EMI, that is Electro Magnetic Induction and Faraday’s Laws of ElectroMagnetic Induction.
Broadly, Electromotive Force is the force that moves an electric charge. Such motion is a current. Discovery of current was as important for progress of human society as the discovery of Fire thousands of years back or the construction of a steam engine by James Watt. Current electricity was the newest method of dealing with power and energy in the nineteenth century that made two things possible, -- first to instantly switch power on and off and later to transfer power to distant places -- this was something unknown before. Both these possibilities have greatly transformed the human life style.
Elecro Motive Force can be provided by various devices like voltaic cells, thermoelectric devices, solar cells and the fuel cell.
Another completely different source of EMF is the phenomenon of electromagnetic induction which is used in electrical generators, transformers, and electrical motors.


Volta’s pile
Let us briefly see the historical context. In 1800, nearly 210 years back, Volta created the historic Voltaic pile.



Taking clue from Galvani’s experiments, he arranged several pairs of alternating copper and zinc discs which he called electrodes in a pile. All discs were separated by cloth soaked in brine which served as electrolyte conductor to increase the conductivity inside the pile. When he connected the top and bottom discs by a wire, an electric current flowed through the wire.

The strength of such pile is expressed in terms of electromotive force, or EMF, whose unit is volts. You have guessed it right that the name of unit of EMF is in honour of Volta. Volta also measured the characteristic EMF of different pairs of metals in place of Cu and Zn. We now understand that the phenomenon in the voltaic piles or their refined mode, the household battery. The electric potential difference is created by separation of positive and negative charges, as a result of chemical reaction between electrodes and electrolyte.

Being a ‘potential ’, an EMF can drive a unit charge. Outside the circuit it will drive the charge from an electrical terminal with a higher potential to another terminal with a lower potential to do an amount of work. This idea is like pumping water up into a tank, from where it can be distributed from high to low potential. However, first the pump has to push water from lower to higher potential, that is, do some work. Similarly, inside the cell, work will be done and the electric charge will be pushed from lower to higher potential.

Let us therefore define EMF as the external work done per unit of charge leading to an electric potential difference across two terminals of a battery, or some such apparatus.Thus,
E = dW/dq

The electrical potential difference thus created would cause the current if an external circuit is attached to the source of emf.
Inside the cell, the chemical reaction will push a positive charge from a point of low potential to a point of high potential. And in the process, will performs work dW on that charge to move it to the high potential terminal.
In the open-circuit case, the reactions at the electrode–electrolyte interfaces will continue to separate the charges and to provide the EMF until the electrostatic field from the separated charges is sufficient to arrest the flow of incoming charges. This is why an open circuit battery will not drain out early. That is also why it is recommended to open the battery in cars when you know that 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 where electron are gained and 1 equation for the oxidation reaction in which electrons are given away.
• The number of electrons gained in the reduction half reaction must equal the number of electrons lost in the oxidation half reaction
• However since the elements of the electrode pair are different, the internal energy level of the element giving away the electron is different than the internal energy of the element accepting them. This is the source of energy inside the cell which makes possible the (internal) pushing of charge from the lower-potential-terminal to the higher-potential-terminal. The higher the energy per reacting charge (electron), the higher the potential it can be pushed to, before the reaction reaches an equilibrium with the EMF, and stops.
• The cell's emf is calculated by adding together the E values for each half reaction:
Ecell = Ereduction + Eoxidation
• As the cell operates, the reactants are used up causing the emf to decrease.
• Following are some typical half electrode potentials --

K+ + e -2.92 V
Al3+ + 3e -1.66 V
Zn2+ +2e - 0.76 V
Ni2+ +2e - 0.23 V
Cu2+ +2e + 0.34 V
Ag+ +e + 0.80 V

Thus a typical Cu-Zn cell will give emf of 1.10 V whereas Ag-Zn cell will give 1.56 V and Cu-Al will give 2.00 V

Some modern sources of emf are a solar cell or photodiode which uses light as the external source of energy. In thermionic emissions it is the thermal energy and in fuel cell it is again the chemical energy.

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EMI
Having understood this much about emf and Volta’s batteries, we come to the most interesting consequential development out of them, namely the discovery of electromagnetic induction by Faraday in 1831. We can recall that though static electricity and magnetism were known to humanity for many decades, the discovery of CURRENT was new and many scientists rushed to experiment with it. Among them, Oersted had observed and reported that a magnetic needle kept near a current switch flickered when the current was either switched on or off. So if a current can influence a magnet, will not a magnet influence the current?

Faraday observed that whenever the magnetic flux changes, it gives rise to a current – meaning that a changing magnetic flux is a source of emf.



Now magnetic flux can be changed either by moving a magnet, say inside the coil of a metallic conductor or by moving the coil between two fixed magnetic poles.
In its simplest fom, Electro Magnetic Induction produces or induces a 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 magnetic flux through the circuit.
In other words, in any closed circuit such as a loop of a wire, when the magnetic flux through a surface bounded by the conductor changes, there will be an induced emf and a resultant current.
A corollary from Faraday's Law was given by Lenz, which is analogous to Newton’s third law of action-reaction. Lenz's law says:
"An induced current is always in such a direction as to oppose the motion or change causing it"
Thus, for a loop we can write --
E = - dΦ /dt
E is the electromotive force (emf) in volts
Φ 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
E = - N.dΦ /dt
where N is the number of turns of wire
The opposion created by induced current gives 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. The name henry was given to the unit of inductance in the honor of Henry, a contemporary scientist who also accomplished lot of studies on the subject.

What is the most significant aspect of Faraday’s discovery?
On application side, it tells us -- move a magnet and you can produce a current – thus we see that while Volta discovered how chemical energy is converted to electrical power, Faraday’s discovery was a way to convert mechanical energy into electrical power. This led to a whole range of generators, electric motors, transformers and a new branch named electrical engineering. As I earlier mentioned, unlike other known sources of power, the electrical power available in terms of current, could be transported to long distances and made available there. This had far-reaching consequences.

Let us learn about them.
In physics there is a trick to understand many phenomena -- always think in terms of the pair Effort and flow. Their product is power.
• Thus, 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
• On the other hand, if the emf generated across the conductor is E then by definition,
• E = Blv. And,
• Power = emf x current = Blvi
Just by remembering these concepts , you can understand a lot about power generation.
Electrical Generator and Motor
Consider two poles of a magnet between which a coil of wire is rotated by using mechanical energy. The two ends of the coil are joined to two split-rings which are insulated from each other and from the central shaft. Two collecting brushes (of carbon or copper) press against the slip rings. This is an Electrical generator because the varying magnetic field will create an electric field due to electromagnetic induction, which in turn will generate emf between generator terminals. The special arrangement of split-rings, brushes and slips allows to gather the emf on the terminals. Charge separation takes place due to 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, but when a load is attached, this voltage can drive a current.

A motor

A motor is essentially same arrangement as a generartor. When we use mechanical power to move the coil and generate emf on the terminals, it is a generator. But if we use a DC voltage supply as input, the contacts at the brushes will make the coil to rotate, which will create mechanical motion. As the motor is turning, it also acts as a generator and generates a "back emf". By Lenz's law, the emf generated by the motor coil will oppose the change that created it. If the motor is not driving a load, then the generated back emf will almost balance the input voltage and very little current will flow in the coil of the motor. But if the motor is driving a heavy load, the back emf will be less and more current will flow in the motor coil and that electric power being used is converted to the mechanical power to drive the load.The motors inside all domestic appliances which we see daily such as a fan, rotor, grinder etc work on this principle .

AC Generator and Motor
A hand-cranked generator can be used to generate AC voltage which will further turn a motor. This is an example of energy conversion from mechanical to electrical energy and then back to mechanical energy.
Mutual Inductance
When two coils are placed nearby, a change in current through one will change the magnetic flux and such a change will induce a current in the second coil. But the current in the second coil also being changing will have a reciprocal effect on the current in first coil. This is called mutual inductance.

Transformer
Imagine two coils wound on two arms of a core made of iron which allows smooth passage of magnetic flux. If an AC current is passed through one coil, called primary winding, then an AC current will be generated in the second coil. If the number of loops in the secondary winding is less, then the voltage generated across the coil will also be less. But the current generated will increase such that the power in first coil is same as the power in second coil except for negligible energy losses in the system. This is called transformer and depending on whether voltage in secondary circuit is less or more it is called step-down or step-up transformer.

Thus transformer is a unique way of transferring electric power from one system to another. This is used for power transmission. You step up the power, thus increasing voltage but reducing current. Then when you transmit the power, ohmic losses will be less as the current is low. At the other end you use a step down transformer to get a normal voltage of 220 volts. This is why transmission is done by high tension wires that is, wires carrying a very high voltage current.

Self induction –
Just as current is induced in the second coil kept nearby, similarly a voltage is also generated in the wire which carries the varying current because the changing magnetic flux has impact on the wire too. This is called Self inductance. The induced emf will tend to oppose the current which created it. Net effect is some kind of resistance to the current which is called inductive resistance as opposed to ohmic resistance.
The voltage generated by self induction due to verying current can be written as
V = L di/dt
Where
V = the induced voltage in volts
L = the value of inductance in henries
di/dt = the rate of change of current in amperes per second.

The term inductor is used to describe a circuit element possessing the property of inductance and a coil of wire is a very common inductor. In circuit diagrams, a coil or wire is usually used to indicate an inductive component.

Formal definitions of electromotive force
Inside a source of emf in open-circuit condition, the 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 the internal path travelled by the charges between two terminals A and B. Mathematically ---


where Ecs is the electrostatic field created by the charge separation, dℓ is a small section of path from terminal A to terminal B. This equation applies only to locations A and B of the terminals and inside the source of emf. For the closed loop, the integral will be zero (???).
However if the closed path is in the presence of a varying magnetic field, then the integral of the electric field around the closed loop will be nonzero; because of the "induced emf"
Now 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. We must remember 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).
Hence for an arbitrary source of emf where flux is changing and path is also moving,

+ some correctional effect for chemical and Thermal forces.
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Maxwell's equations (cut paste) Faraday's experiments
The applied aspect of Faraday’s discovery of electromagnetic induction led to a new branch of electric engineering. But the theoretical study of it led to the invention of electromagnetic theory of light – that is how light, or more appropriately how energy travels as electromagnetic waves and this further led to the theory of relativity.

Faraday had tried to explain the phenomenon by conceptualising lines of force, and flux density. Let me remind you of a childhood pass time. You take two large pieces of broken bangle, hold the middle of one on a candle flame so that the glass bends till the two open ends meet. Then you weave another piece through this loop and again bend it on the flame at its middle section -- till its ends also meet. Thus you have two bangle loops woven into each other. This is what Faraday visualised as the loop of the conducting wire and the invisible loop of magnetic flux. This conceptualisation was very useful for developing the vector calculus to get mathematical expression for Electro magnetic Induction.

Through his equations—Maxwell demonstrated that electric and magnetic fields travel through space in the form of waves, and when he theoretically calculated the speed, he found it in the close range of the speed of light. He concluded that electricity, magnetism and even light are all manifestations of the same phenomenon, namely, the electromagnetic field. His quantitative connection between light and electromagnetism is considered one of the great accomplishments of 19th century mathematical physics.
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