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Inductance is the innate ability of a conducting object because of which it opposes even the slightest change in the amount of electric current that is flowing through it. When we allow the electric current to flow through a conducting body, we allow it to create a magnetic field around it. If we try to change the amount of current, subsequently, the magnitude of the magnetic field will also change. As per Faraday’s law of induction, if there is a change in the magnetic field passing through the conducting body, then the body will induce an electromotive motive force within itself. This paragraph will help us move forward into topics like the effect due to gravitational force and the role of earth magnetic field in induced emf.
Placing A Conducting Rod in Earth’s Magnetic Field
This section will provide you the idea of what will happen if a moving conducting rod is placed in the Earth’s magnetic field.
#Note: – We will consider both the components of the Earth’s magnetic field until and unless it is mentioned explicitly in the problem that the conductor is placed on the Equator (Horizontal component becomes zero) or at the North or the South Pole(Vertical component becomes zero). And the direction of Earth’s magnetic field is from the geographic North to the geographic South.
Case1. If the rod is placed in the horizontal plane and its direction is also horizontal. The velocity of the rod is perpendicular to its length.
Subcase1. If the rod’s ends are in the West-East direction.
Since the length of the rod is perpendicular to the velocity, you might think that the rod will definitely induce some emf, but that will not happen because the direction of the magnetic field is from the South to the North, which is already in the plane in which the rod is moving (rod’s velocity). The direction of the speed and the direction of the earth magnetic field will make 180 degrees with each other. Hence, there will be zero induced electromotive force in the horizontal direction.
Emf horizontal = 0 [Bhorizontal II v]
But, the earth magnetic field will have a vertical component that will form a mutually perpendicular direction with the length of the rod and its velocity. Therefore, an electromotive force will be introduced due to inductance cause by the perpendicularity of factors.
Subcase2. If the rod’s ends are in the South-North direction.
Since, the direction of the earth magnetic field is from South to North, and the direction of the rod placed is also the same, it can be placed either in the North to South direction or South to North, only change will come in the direction of the induction emf but the value will still be zero because they are parallel.
Emfhorizontal = 0 [Bhorizontal II length]
If we will calculate the induced emf by considering only the vertical component of the earth magnetic field, then we will understand that all the three factors are mutually perpendicular.
Emfvertical = Bvertical vl
Case 2. If the rod is placed in the vertical plane and its direction is also vertical. The velocity of the rod is perpendicular to its length.
Subcase1. If the rod moves in a West-East direction.
As the rod is hanging vertically and the direction of the vertical component of the earth magnetic field is also vertical, they will form a parallel pair. Therefore, the induced emf generated due to the vertical component of the magnetic field when the rod is also placed vertically is zero.
Emfvertical = 0 [L II Bvertical]
Now, we will observe the horizontal cause for generation of induced emf. We can see that the length of the rod, velocity of the rod, and the horizontal component of the earth magnetic field are mutually perpendicular with each other.
[Emfhorizontal = Bhorizontal vl]
Subcase2. If the rod moves in a South-North direction.
If the rod is moving in the South-North direction or the North-South direction, it will not change the magnitude of the induced emf because the induced emf will be zero. Because the velocity of the rod and the direction of the horizontal component of the earth magnetic field is either parallel (zero degree in case of South-North) or anti-parallel (180 degrees in the case of North-South). Only change will come in the clockwise or anti-clockwise direction of the induced emf inside the rod.
Emfhorizontal = 0 [Bhorizontal II v]
Now, if we consider the vertical component of the earth magnetic field it is in the direction from the South to North. Similarly, since the rod is hanging vertically this means that the length of the rod and vertical component of the magnetic field will be parallel or anti-parallel.
Hence, no induced emf can be observed in this subcase.
Emfvertical = 0 [Bhorizontal II l]
Conclusion
We discussed how different orientations can affect the amount of electromotive force that can be induced due to induction generated by the moving conductor in the earth magnetic field. The gravitational force is irrelevant in the case of the emf induction process caused by the originating earth magnetic field from the South Pole till the North Pole.
