Showing posts with label EMI. Show all posts
Showing posts with label EMI. Show all posts

Electromagnetic Induction Complete Lesson and Alternate Current

There is a induced EMF and induced current developed in every coil in which there is a change in the current. The magnitude of this current depends on the number of the turns in the coil and also on the rate of change of the flux. If the change in the field happens in the same coil, the induction is called self induction and if that is happening in the other coil due to the change in the field due to the first coil, then the induced EMF is called mutual induction. We can find the direction of the induced current using Lenz law.

This post is a collection of different topics done in this particular lesson in the given order. This is the list of topics done in this module.

Faraday’s Experimental Observations about EMI

Lenz Law and Electromagnetic Induction

Self Induction and Mutual Induction

Induced EMF due to Variable Current and Moving Conductor

Induced EMF due to Motional Conductor


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Finding Self Induction and Inductors in Series and Parallel

Finding self-inductance of a coil

Self inductance is the property of a coil by virtue of which it opposes the change in the magnetic flux causing it. A galvanometer connected to the circuit of the coil shown the deflection change only when there is a change in the switch mode that is during on and off mode. It indicates that the induced EMF is generated only during that time.

The magnitude of the induced current developed in a coil is directly proportional to the magnetic flux generated in that coil. We can eliminate the proportionality using a constant called self inductance coefficient.

We can find the magnetic flux in a coil using the concept that it is the dot product of magnetic field induction and area of cross section.


Further using the concept that the flux is the product of self induction constant and induced current, we can find the self induction constant as shown in the diagram below.


Similarly we can also find the mutual induction coefficient as shown in the diagram below.


Inductance coils connected in series and parallel

We can measure the effective induction coefficient when the coils are connected in series and parallel. When the coils are in series, the current in each coil is same to the current passing in the circuit. We also know that the emf of the circuit is the sum of total emfs in the circuit.

Using that concept we can find the effective coefficient when the coils are connected in series as the sum of individual coefficients. When the coils are connected in parallel, the current of the system is shared across the coils and emf of the circuit is similar to the emf of the coil.

Thus we can measure the effective coefficient as shown in the diagram below.




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Induced EMF due to Motional Conductor

Induced EMF in a rod moving through a U shaped container


Let us consider a magnetic field acting into the paper. Let us assume a rod of known length is moving in that field across a container with a known velocity.



We can draw an equivalent circuit and find the EMF developed in the circuit as shown below.


If a rod is moving with a known velocity and with an angle to the magnetic field, we can find the magnitude of induced EMF developed in the circuit as  shown in the diagram below.


If the same rod is bent at the middle and it is moved through with a known velocity, we can measure the induced EMF as shown in the diagram below.


When a conductor of known length is moving in a electric circuit with a known velocity, under the influence of the magnetic field, an induced EMF is generated and the corresponding force and the power generated there can be measured as shown in the diagram below.



The equation for the force and power are as shown in the diagram below.



Motional EMF generated in a rotating rod or bar

Let us imagine a rod of known length is in a magnetic field and it is passing current through it. Let it is rotated in the field with a known angular velocity. Let us assume that it has turned only through a known angle and hence some area of the sector is covered. Basing on that, we can measure the magnetic flux and magnetic field induction and induced EMF as shown in the diagram below.




The magnitude of the EMF generated in this process is independent of the spokes the wheel has. In this case we are measuring the EMF due to a wheel rotating in the magnetic field.



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Induced EMF due to Variable Current and Moving Conductor

When a circular coil placed above a current carrying conductor

Let us assume a circular coil above a current carrying conductor.Let us assume a case when a constant current is passing through the conductor. As constant current produce a constant magnetic field, there is no change in the field. Hence no induced EMF is generated in the closed coil.

Let us consider one more case where the conductor is carrying a increasing current. According to right hand thumb rule the direction of magnetic field around the current carrying conductor is outward. To oppose the generated magnetic field in the current carrying conductor, an inward magnetic field is generated in the coil nearby. Thus a clock wise current is generated in the closed coil.


Let us consider another case where the current in a straight conductor below the coil is decreasing. This generates a magnetic field inward and hence the magnetic field in the coil is outward. Thus the current in the coil is anticlockwise.

In another case let us assume an electron passing through a straight conductor. Thus the current in it is in the opposite direction. The magnetic field around it is in the clock wise direction. The induced emf in the closed coil to oppose it, anti clockwise current and north pole is generated on the face of the coil.


Motional EMF generated in a straight conductor when it is moved in a magnetic field with a certain velocity

We can move a current carrying conductor of known length with certain velocity in a magnetic field.


This rod will experience a force and we can measure it using the rule that we know all ready. We can also find the direction of the force experienced by the conductor using the Fleming left hand rule.


We can find the expression for the induced emf and current as shown in the diagram below.




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Self Induction and Mutual Induction

Basing on the experimental results, Faraday made some conclusions. Experimental arrangement can be shown below.

They are
1.   When a magnetic flux linked with a  closed circuit changes, an induced EMF and induced current is developed in that closed circuit.

2.   Induced EMF exists until there is a change in the magnetic flux.

3.   EMF developed in the closed circuit is directly proportional to the rate of change in the magnetic flux.


If the flux is due to the number of coils, there is EMF in each coil and the total EMF is the sum of all of them. We can write magnetic flux as the dot product of magnetic field induction and area of cross section. As they are in the same direction, the cos angle is equal to one and maximum. The total magnetic EMF can be written as shown in the figure.



We can defile self induction coefficient as shown below. It is simply the magnitude of the induced EMF in a closed circuit when the rate of change of flux is one unit.



To find the direction of the induced EMF, we can use a law called Fleming right hand thumb rule. According to this rule,

If a fore finger indicates the direction magnetic field, thumb indicates the direction of the conductor then the central finger indicates the direction of the induced current in the closed circuit.


We can also find out the charge and the induced current at a given circuit due to induction as shown in the diagram below.




Problem and solution

Magnetic flux is given in the problem and we need to find induced current in the closed circuit. We can do that by differentiating the flux with time so that we get induced EMF in the circuit. Further we can write that induced EMF as the ratio of induced current and resistance. By substituting the resistance value in the circuit, we can measure the current in the circuit as shown in the diagram below.



Mutual induction

This is the induced EMF generated in the secondary coil due to change in the magnetic flux in the first coil. The first coil is having a battery and a key to control the flow of current. The second coil consists of a galvanometer. When the switch in the first coil is just switched on or off, change in the reading of the galvanometer is noticed. Thus emf is developed in the second coil due to change in the flux in the first coil.


Basing on this concept, we can define the mutual inductance and its coefficient as shown in the diagram below.


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Lenz Law and Electromagnetic Induction

To understand the generated EMF, we have a rule called Lenz rule. This is a fundamental rule and it works basing on law of conservation of energy.

According to the Lenz law, a changing magnetic field produces a induced EMF and induced current in a closed coil. This induced EMF opposes the change in the magnetic flux that creates it.

If we are moving a magnet towards a closed coil, it generates a change in the magnetic field. If you are moving a north pole towards the coil, the current is generated in the closed coil such that it generates another north pole on the face of magnet coming towards it with North Pole so that it opposes the change.



If we are getting south pole of a magnet towards a closed coil, the induced current in that closed coil intern generate another magnetic field with south pole so that it opposes the change in the magnetic flux.


Thus it totally tells us that the induced emf and induced current opposes the change in the magnetic flux that is causing it and that can be shown below in the diagram.

If a bar magnet is coming towards a current carrying coil in the perpendicular plane, an induced EMF is generated. The generated potential difference always oppose the change in the magnetic flux. Thus when north pole of the bar magnet is approaching it, north pole is formed over the surface and anti clock wise current is generated. Even when the north pole is going away from the coil, to oppose that change a south pole is formed on the face of the coil and hence a clock wise induced current is generated there. In that sense, the magnet always experience a acceleration less than the acceleration due to gravity.


If the coil is not a closed coil, there is no induced EMF and hence, the magnet falls through it with an acceleration equal to acceleration  due to gravity.


The magnitude of induced EMF varies even with the variation of the temperature of the coil. If the temperature increases, the resistance of the coil decreases and hence induced emf increases.



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Faraday’s Experimental Observations about EMI

If there is a change in the current in the circuit with time, there will be a change in the magnetic field around the coil and it produce a induced EMF  in the coil. To study the EMF, Faraday has made some experiments and here we are going to study that experimental observations.

We can also understand the magnetic field induction in some other way. In the previous case, experiencing the change in magnetic flux is for a very small time. It is just during the switch on and off process that is for a very small interval of time. To experience it in a very detailed way, let us have a closed coil with a galvanometer. Let us consider a magnetic needle and if you are keeping the magnetic needle at rest, no EMF is generated.


When the magnetic needle is moved towards the coil, the galvanometer moves in one direction and EMF is generated.


Even when the magnet is moved in the opposite direction, the galvanometer deflects in opposite direction and it indicated that the current is developed in the opposite direction.


We can observe the same even when the magnet is in the state of rest and the coil with galvanometer is either moved towards or away from the stationary magnet.

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Electromagnetic Induction Reasons and Explanations

Electromagnetic induction is a phenomenon of generation of electric current and EMF in a closed circuit when the magnetic flux linked with the closed circuit changes.

Michelson Faraday discovered that the change in magnetic flux in any closed circuit generates electromagnetic force or a potential difference in a closed circuit.

To explain this we can consider a small experiment consisting of two coils wound around a wooden core. The first coil consists of a battery and key. The second coil consists of galvanometer. It is experimentally observed that as long as constant current is passing in the first coil, the galvanometer shows the zero deflection. It means that there is no EMF generated in the secondary coil.

When the key the first closed coil is just closed, galvanometer shows some deflection and some EMF is generated. It is also noticed that even when the switch is just opened, galvanometer shows the deflection in the opposite direction. It means EMF is again generated and the current is generated in the opposite direction.


It can be noticed that when you just switch on or off the current in the first coil, there is a change in the current in that circuit. The current in the coil changes from zero to maximum value in small time. During this small time, the magnetic field around the closed coil changes. This changing magnetic field in the first coil produce a electric current and EMF in the neighboring circuit.

Magnetic flux

The number of magnetic lines of force passing through a given area of cross section normally is called magnetic flux and the magnetic flux per unit area is called magnetic induction. Magnetic flux is measured with a unit called weber and magnetic induction is measured with weber per meter square.


The magnetic field induction also depends on the angle between the magnetic flux and the area of cross section and it varies basing on it.


We can find its value for different angels as shown in the diagram below.


Its variation with different factors can be studied as shown in the diagram below.



The explanation can be further extended as shown in the diagram below.

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