What is Electro Magnetic Induction:
Introduction of electromagnetic induction and alternating current
Electromagnetic Induction is a phenomenon in which electric emf is induced across a coil whenever a changing magnetic flux links this coil and the electric current flows
Michael Faraday, while performing an experiment in magnetism found that a small emf was set up in a nearby coil and a surge of electric current he noticed in it. He was surprised to note this observation that was just the reverse of that which Oersted established in 1820 as the magnetic Effect of Currents. Later, he presented this observation as a phenomenon called “Electromagnetic Induction.”
What is Magnetic Flux in Electromagnetic Induction and alternating current
The Magnetic flux through a surface, placed in a magnetic field in a direction normal to it, is defined as the total number of field lines crossing it and is equal to the product of the component of the magnetic field normal to the surface and area of the surface.
Thus, the magnetic flux through a surface placed in a magnetic field is defined as the surface integral of the normal component of the magnetic field taken over the entire surface.
Case 1: When the magnetic field is perpendicular to the surface area
From the figure above, we see that the surface area is placed inside the magnetic field B such that the direction of magnetic field is perpendicular to the surface area and therefore, theta is zero degree that implies that Cos0= +1.Therefore, the magnetic flux linking the coil is maximum when the magnetic field is normal to its surface and is given by the product of the magnitude of the magnetic field and area of the surface => Flux = B A
Case 2: When the magnetic field is parallel to the surface area.
From the figure above, we see that the surface area is placed inside the magnetic field B such that the direction of the magnetic field is parallel to the surface area and therefore, theta is 90° which implies that Cos 90° = 0Therefore, the magnetic flux linking the coil is minimum (zero) when the magnetic field is parallel to its surface and the product of the magnitude of the magnetic field and area of the surface is zero => Flux = 0
Units of Magnetic flux in Electromagnetic Induction and alternating current
- S I units of magnetic flux is weber
Flux = B A = 1 Tesla (T) x 1 m2 = 1 weber, Thus, the magnetic flux linking a coil is said to be one weber, when it has an area of one square meter is placed in a magnetic field of one Tesla.
2.C.G.S units of magnetic flux is maxwell.
Flux = B A = 1 Gauss (G) x 1 cm2 = 1 maxwell, Thus, the magnetic flux linking a coil is said to be one maxwell, when it has an area of one square centimeter is placed in a magnetic field of one Gauss.
Relation:
1 weber = 1 T x 1 m2 = 104 Gauss x 104 cm2 = 108 Gauss x cm2 = 108 maxwell => 1 Wb = 108 maxwell
Faraday’s Experiments
Michael Faraday, a pioneer scholar in the field of magnetism performed a series of experiments in 1830. The following three experiments, their observations and the explanations led him to the discovery of the phenomenon of electromagnetic induction.
Experiment No. 1 When the strength of the magnetic field undergoes a change
Consider two coils P and S wound on an iron rod that are electrically insulated from each other. A sensitive galvanometer is connected to the coil S while an electric cell and a taping key K are connected to the neibouring coil P. Michael Faraday observed that a deflection is produced in the galvanometer when the tapping key is pressed. When the taping key is released, deflection is again produced, but in the opposite direction. The Galvanometer does not show any deflection when the taping key is kept. Is kept pressed.
Explanation
As the tapping key k is pressed with coil P, the electric current in this coil starts rising to result in an increasing magnetic field. Since coil S is inductively connected to that of P, therefore, an increasing magnetic field links coil S and so an emf is induced across it, causing an induced current to flow in coil S as detected in the galvanometers.
On the other hand, when the key is released, the current starts decreasing and the decreasing magnetic flux links the neighboring coil S, so the current is again induced but in opposite direction. No emf is induced when either the current in coil P is maximum or zero. It is here concluded that the emf is induced only when the magnetic flux linking the coil changes and becomes zero as soon as the magnetic flux linking the coil stops changing.
Experiment no. 2 When a magnet is moved towards the coil or away from the coil at rest
When a magnet with its N-pole facing the coil is moved away from the coil, the galvanometer shows the deflection indicating that the emf is induced across the coil and hence induced current flows through the coil. The same result is observed when the magnet is moved towards the coil but the current now flows in opposite direction.
This is because the magnetic field and hence the magnetic flux linking the coil undergoes a change which causes the emf to be induced. Faster the magnet is brought near the coil or away from the coil, more will be the emf induced and vice versa.
Experiment 3. When a coil moves in a uniform magnetic field
Let us suppose that a rectangular coil MNLK is placed in a uniform magnetic field perpendicular to the plane of the paper and directed away from the reader in the region ABCD shown by the cross lines (x). When the coil is moved to the right-hand side, the galvanometer shows no deflection so long as the entire coil remains within the magnetic field.
On the other hand, when the coil is moved such that a part of the coil is outside the field and the other part is inside the magnetic field, the deflection in the galvanometer is observed. This is because the magnetic flux in this case linking the coil is changing, as a result the emf is induced which is called motional emf.
What are Faraday’s Laws of Electromagnetic Induction
Michael Faraday got legitimized the observations and the outcomes of his experiments in electromagnetism in the form of laws called Faraday’s Laws of Electromagnetic induction.
Faraday’s 1st Law of Electromagnetic Induction:
This Law states that whenever, a changing magnetic flux links a coil, a loop of wire, or an electric circuit, an emf is induced and an electric current starts flowing through it. The emf so produced is called induced emf and the resulting current is called as induced current
How we can change the magnetic flux linking the coil
- By moving the coil towards the magnet or away from the magnet.
- By moving the magnet towards the coil or away from the coil.
- By rotating the coil in a uniform magnetic field.
- By changing the area of the coil placed in the magnetic field.
Faraday’s 2nd. Law of electromagnetic Induction:
The induced emf in a coil persists/lasts so long as the magnetic flux linking it continues to change and becomes zero as the magnetic flux linking to the coil stops changing.
Faraday’s 3rd. Law of electromagnetic Induction:
The magnitude of the emf induced in a coil is directly proportional to the rate of change of magnetic flux linking the coil.
What is Motional EMF in Electromagnetic Induction and alternating current
Motional EMF is defined as the emf induced across a conductor of certain length, when moved inside a uniform magnetic field whose magnitude is equal to the product of the magnetic field B, length of the conductor l, and the velocity of the conductor with which it moves in the magnetic field.
Thus, e = Blv
Let us suppose that a U-shaped rail of wire NMPO is placed in the uniform magnetic field B perpendicular to the plane of paper and directed away from the reader as shown by the cross lines (x). A conductor AB of length l can be moved over this rail of wire. Consider that this wire is pushed
Let us suppose that a U-shaped rail of wire NMPO is placed in the uniform magnetic field B perpendicular to the plane of paper and directed away from the reader as shown by the cross lines (x). A conductor AB of length l can be moved over this rail of wire. Consider that this wire AB is pushed to the right side of the field with a speed v for a time dt second so that it acquires a position CD. Now the change in the area will be dA = Area MCDP – Area MABP
The rate of change of area of the closed loop dA/dt = (Area MCDP – Area MABP)/dt
dA/dt = Area ACDBA /dt = (AB x BD)/dt = l x v dt/ dt = l v
According to the Faraday’s 3rd Law of electromagnetic induction, the induced emf will be emf = – B (dA/dt)
e = – B l v
Negative sign is in accordance of Lenz’s Law
What is Lenz’s Law? How it is Consistent with Conservation law of energy in Electromagnetic Induction and alternating current
Lenz’s law states that whenever a changing magnetic flux links a coil, the induced current produced in the coil always flows in such a direction that it opposes the change, or the cause that produces it.
Faraday’s Laws of Electromagnetic Induction
Consider that a coil connected with a sensitive Galvanometer G is placed near a bar magnet whose N-pole is facing the coil as in Fig.10 When the magnet is moved towards the coil, a changing magnetic flux links the coil and as per the laws of electromagnetic Induction, the emf is induced and the electric current starts flowing in the coil in the direction as shown in the fig- 10.
According to the laws of the magnetic effect of current, the electric current induced in the coil will produce a magnetic field whose direction as per Right Hand Thumb rule will be such that the end of the coil towards the magnet will become an N-pole exerting the force of repulsion on the bar magnet. Therefore, the current in the coil is induced in such a direction that the cause of its production is opposed.
Now, the magnet is moved away from the coil. The changing magnetic flux will link the coil and as per the laws of electromagnetic Induction, the emf will be induced and the electric current starts flowing in the coil in the direction as shown in the fig- 11
According to the laws of magnetic effect of current, the electric current induced in the coil will produce a magnetic field whose direction as per Right Hand Thumb rule will be such that the end of the coil towards the magnet will become N-pole exerting the force of attraction on the bar magnet. Therefore, the current in the coil is induced in such a direction that the cause of its production is opposed.
From these two activities, we conclude that the motion of the magnet towards the coil or away from the coil is opposed by the direction the current induced in the coil which is the cause of its production. In order to overcome this force of opposition, we have to do some mechanical work. It this mechanical work which is converted in to the form of electrical energy. Therefore, the Lenz’s law is in accordance with Conservation law of energy.
What are the eddy currents in Electromagnetic Induction and alternating current
When a magnetic plate is placed in a rotating magnetic field or the metallic plate is rotated in a uniform magnetic field, then the electric currents are induced in the surface of the plate in the form of closed loops. These currents are called eddy currents due to their eddy or loop nature or Foucault currents after the name of their discoverer Sir Foucault
Thus, the eddy currents are the electric currents induced in a conductor when placed in a varying magnetic field and can not be extracted out of the metallic body of the conductor.
Experimental setup to prove the existence of Eddy currents in Electromagnetic Induction and alternating current
Experiment
Take a solenoid inserted with a soft iron core inside it and connected with a source of emf. A metallic disc is placed over the cross-sectional face of the soft iron core as shown in fig. 13 We observe that the metallic disc will fly off and thrown in to the air as the circuit is switched on.
The electric current starts growing in the solenoid as the circuit is switched on which causes an increasing magnetic field along the axis of the solenoid. Thus, the magnetic flux will link the disc that changes from zero to some maximum value. As a result, the induces current (eddy currents) are set up in the disc in such a direction that its cause is opposed, thereby, the disc is thrown away.
Applications of Eddy currents in Electromagnetic Induction and alternating current
- Induction motors
A rotating magnetic field is produced by means of two single-phase currents. A metallic rotor placed inside the rotating magnetic field starts rotating due to the large eddy currents produced in it. These motors are commonly used in fans
- Induction furnace
In an induction furnace, very high temperature can be produced by producing large eddy currents. The high Frequency eddy currents are preferred because of the reason that the heating effect of current is proportional to the square of the frequency of the current.
- Diathermy.
Since Eddy currents have the property of heating effect, therefore these currents are now being used for deep heat treatment called diathermy.
- Energy meters
In Energy meters, the armature coil carries a metallic aluminium disc, which rotates between a pair of poles of permanent horseshoe magnets. As the armature rotates, the current induced in the disc tends to oppose the motion of the armature coil. Due to this braking effect, the deflection is proportional to the energy consumed.
- Electric brakes
The principle of Eddy Currents is used as the brakes in the trains. A metallic drum is coupled with the wheels of the train, so that when the train runs, the drum also rotates in order to stop the train. A strong magnetic field is applied in the rotating drum. The large eddy currents produced oppose the motion of the drum, since the drum is connected to wheels of the train, the later comes to a halt.
- Electromagnetic damping.
The oscillations of the coil of a galvanometer, can also be stopped by short circuiting the two ends of the coil through a tapping key. When the key is pressed, the coil circuit is closed and the eddy currents are produced due to the motion of the coil inside the magnetic field, produced by the magnet of the galvanometer. According to Lenz’s law, the direction of the eddy currents is such that it opposes the oscillation of the coil. This opposition is in the form of electromagnetic damping.
What are the undesirable Effects of Eddy currents in Electromagnetic Induction and alternating current
As the resistance of a metallic conductor is quite low, therefore, the Eddy currents produced is of quite large magnitude. As per the principles of Joule’s heating effect of current, a considerable amount of heat is produced in the conductor. If the large eddy currents are allowed to produce in the core of a choke coil, core of the transformer, dynamo, etc., a significant part of the electric energy is converted into energy as a waste product. It may produce undesirable effects.
Summary of Electromagnetic Induction and alternating current
- When a surface is placed in a magnetic field, the magnetic flux linked with it is maximum, when it is rotated in the direction perpendicular to the direction of magnetic field, and becomes zero when it is in the direction parallel to the direction of magnetic field.
- The magnetic flux through a surface is equal to the product of the magnitude of magnetic field and the area of the surface when the surface is positioned perpendicular to the magnetic field.