state and Prove the Faraday Law of electro magnetic induction?
Answers
The law was proposed in the year 1831 by an experimental physicist and chemist named Michael Faraday. So you can see where the name of the law comes from. That being said, the Faraday’s law or laws of electromagnetic induction are basically the results or the observations of the experiments that Faraday conducted. He performed three main experiments to discover the phenomenon of electromagnetic induction.
Faraday’s Experiment:
Relationship Between Induced EMF and Flux:
In the first experiment, he proved that when the strength of the magnetic field is varied then only the induced current is produced. An ammeter was connected to a loop of wire; the ammeter deflected when a magnet was moved towards the wire.
In the second experiment he proved that passing a current through an iron rod would make it electromagnetic. He observed that when there a relative motion exists between the magnet and the coil, an induced electromagnetic force is created. When the magnet was rotated about its axis, no electromotive force was observed but when the magnet was rotated about its own axis then the induced electromotive force was produced. Thus, there was no deflection in the ammeter when the magnet was held stationary.
While conducting the third experiment, he recorded that galvanometer did not show any deflection and no induced current was produced in the coil when the coil was moved in a stationary magnetic field. The ammeter deflected in the opposite direction when the magnet was moved away from the loop.
Position of MagnetDeflection in GalvanometerMagnet at RestNo deflection in the galvanometerMagnet moves towards the coilDeflection in the galvanometer in one directionMagnet is held stationary at same position( near the coil)No deflection galvanometerMagnet moves away from the coilDeflection in galvanometer but in opposite directionMagnet held stationary at same position(away from the coil)No deflection in galvanometer
Conclusion:
After conducting all the experiments, Faraday finally concluded that if relative motion existed between a conductor and a magnetic field, the flux linkage with a coil changed and this change in flux produced voltage across a coil.
Faraday law basically states, “when the magnetic flux or the magnetic field changes with time, the electromotive force is produced”. Additionally, Michael Faraday also formulated two laws on the basis of above experiments.
Faraday’s First Law:
Faraday’s First Law of Electromagnetic Induction states that whenever a conductor is placed in varying magnetic field, electromagnetic fields are induced known as induced emf. If the conductor circuit is closed, a current is also induced which are called induced current.
Ways of changing magnetic field:
By rotating the coil relative to the magnet.By moving the coil into or out of the magnetic field.By changing the area of a coil placed in the magnetic field.By moving a magnet towards or away from the coil.
Faraday’s Second Law:
Faraday’s Second Law of Electromagnetic Induction states that the induced emf in a coil is equal to the rate of change of flux linkage. Here the flux is nothing but the product of number of turns in the coil and flux connected with the coil.
Faraday’s law is represented as;
ε=−NΔϕΔt
In any case, Faraday’s law today finds its application in most of the electrical machines, industries and medical field etc.
Additionally, there is another key law known as Lenz’s law that describe electromagnetic induction as well.
While Oersted's surprising discovery of electromagnetism paved the way for more practical applications of electricity, it was Michael Faraday who gave us the key to the practical generation of electricity: electromagnetic induction.
Faraday discovered that when he moved a magnet near a wire a voltage was generated across it. If the magnet was held stationary no voltage was generated, the voltage only existed while the magnet was moving. We call this voltage the induced emf (E).
A circuit loop connected to a sensitive ammeter will register a current if it is set up as in this figure and the magnet is moved up and down:
Magnetic flux
Before we move onto the definition of Faraday's law of electromagnetic induction and examples, we first need to spend some time looking at the magnetic flux. For a loop of area A in the presence of a uniform magnetic field, B⃗ , the magnetic flux (φ) is defined as:
ϕ=BAcosθ
Where:
θAB=the angle between the magnetic field, B, and the normal to the loop of area A=the area of the loop=the magnetic field
The S.I. unit of magnetic flux is the weber (Wb).
You might ask yourself why the angle θ is included. The flux depends on the magnetic field that passes through surface. We know that a field parallel to the surface can't induce a current because it doesn't pass through the surface. If the magnetic field is not perpendicular to the surface then there is a component which is perpendicular and a component which is parallel to the surface. The parallel component can't contribute to the flux, only the vertical component can.
In this diagram we show that a magnetic field at an angle other than perpendicular can be broken into components. The component perpendicular to the surface has the magnitude Bcos(θ) where θ is the angle between the normal and the magnetic field.
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Faraday's Law of electromagnetic induction
The emf, E, produced around a loop of conductor is proportional to the rate of change of the magnetic flux, φ, through the area, A, of the loop. This can be stated mathematically as:
E=−NΔϕΔt
where ϕ=B⋅A and B is the strength of the magnetic field. N is the number of circuit loops. A magnetic field is measured in units of teslas (T). The minus sign indicates direction and that the induced emf tends to oppose the change in the magnetic flux. The minus sign can be ignored when calculating magnitudes.
Faraday's Law relates induced emf to the rate of change of flux, which is the product of the magnetic field and the cross-sectional area through which the field lines pass.
It is not the area of the wire itself but the area that the wire encloses. This means that if you bend the wire into a circle, the area we would use in a flux calculation is the surface area of the circle, not the wire.
In this illustration, where the magnet is in the same plane as the circuit loop, there would be no current even if the magnet were moved closer and further away. This is because the magnetic field lines do not pass through the enclosed area but are parallel to it. The magnetic field lines must pass through the area enclosed by the circuit loop for an emf to be induced.
Direction of induced current (ESBQ2)
The most important thing to remember is that the induced current opposes whatever change is taking place.
In the first picture (left) the circuit loop has the south pole of a magnet moving closer. The magnitude of the field from the magnet is getting larger. The response from the induced emf will be to try to resist the field towards the pole getting stronger. The field is a vector so the current will flow in a direction so that the fields due to the current tend to cancel those from the magnet, keeping the resultant field the same.
To resist the change from an approaching south pole from above, the current must result in field lines that move away from the approaching pole. The induced magnetic field must therefore have field lines that go down on the inside of the loop. The current direction indicated by the arrows on the circuit loop will achieve this. Test this by using the Right Hand Rule. Put your right thumb in the direction of one of the arrows and notice what the field curls downwards into the area enclosed by the loop.
In the second diagram the south pole is moving away. This means that the field from the magnet will be getting weaker. The response from the induced current will be to set up a magnetic field that adds to the existing one from the magnetic to resist it decreasing in strength.