Motional EMF

Motional emf is a process in which an emf is inserted into a conductor as a result of its movement within a magnetic field. Suppose a U-shaped spinning wire is inserted into the magnetic field and a metal rod is placed over the wire. If a metal conducting rod is allowed to go right or left with a U-shaped wire, the emf will be inserted inside that loop. This inserted emf is commonly referred to as motional emf. Many applications of this concept exist, as we will see in the next article (electric blood flow meter).

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To understand electromotive electromagnetic force, let's do something. Let's take a rectangular coil, an L-shaped steel rod, traveling V-speed, passing through magnetic field B. There is a magnetic field somewhere.

Length, speed and magnetic field must always be at right angles to each other. The direction of the magnetic field goes inward. Assume that the steel rod is not rigid which means there is no loss of strength due to sliding and we use the same magnetic field. The conductor rod is moved at a constant speed and placed in a magnetic field.

But 'x' changes over time,

E = -\[\frac{d\Phi }{Bdt} = -\frac{d}{dt} = -\left ( Blx \right ) = -Bl\frac{dx}{dt}\]

E = Blv

The inserted emf Blv is a dynamic electromotive force. We therefore produce the emf by moving the conductor within the same magnetic field. The force required to move the conductor rod into the magnetic field,

P = \[\frac{B^{2}l^{2}v^{2}}{R}\]

There,

B is a magnetic field,

l conductor length

v driver speed

R resistance

The magnetic flux associated with the coil is given by Φ = BA cos θ. We know that cos θ = 0, so Φ = BA. The electromotive power movement can also be described as the Lorentz power that works on free carriers. Lorentz's strengths are in control:

F = qVB

EMF

Any change in magnetic flux induces an emf opposing that change is the process known as induction. The motion is one of the major causes of the process of induction. For example, we can say that a magnet which has moved toward a coil induces an emf and a coil which has moved toward a magnet produces a similar emf. In this section, we will discuss motion in a magnetic field stationary relative to the planet Earth producing what is loosely known as motional emf. There is one situation where we can say there is a motion that generally occurs, called the Hall effect and has already been examined. The moving charges which are moving in a magnetic field experience the magnetic force denoted by F = qvB. Refer to the official website of Vedantu or download the app for an elaborate and comprehensive explanation. 

What is Motional EMF?

The charge which we are talking about in opposite directions and produces an emf = Bℓv. We can generally see that the Hall effect has applications which include measurements that are of symbols which are B and v. We will also notice now that the Hall effect is one aspect of the broader phenomenon of induction and we will conclude that motional emf can be used as a power source. Here we should consider the situation of a rod moving at a speed v along a pair of conducting rails which are separated by a distance denoted by symbol ℓ in a uniform magnetic field B. The rails which are stationary relative to B and are connected to a stationary resistor denoted by R.

Motional Electro-Motive Force

The resistor generally could be anything from a light bulb to even a voltmeter. Let us consider the area enclosed by the moving rod, rails, and resistor. The letter B which we know is perpendicular to this area and we can say that the area is increasing as the rod moves. Thus, here we notice that the magnetic flux generally enclosed by the rails and the rod and resistor is increasing. When the term changes then generally an emf is induced according to Faraday’s law of induction.

Here again, we see that to find the magnitude of emf induced along the moving rod uses the law of Faraday of induction without the sign:

denoted as emf = \[\frac{N\Delta }{\Phi \Delta }\]

Here and below also the term “emf” is the magnitude of the emf. In this equation we have learnt that the equation N = 1 and the flux denoted by Φ = BA cos θ. We have already seen a symbol denoted by letter or symbol θ = 0º and cos θ = 1 since B is perpendicular to A. Now the symbol ∆Φ = ∆(BA) = BΔA since B is uniform. We can see that the area swept out by the rod is ∆A = l∆x. 

Lenz’s Law

Lenz's law of electromagnetic input states that the current induced magnetic field current (according to Faraday's magnetic field) is so precise that the current induced magnetic field contradicts the original magnetic field that it produced. . Guidance for this current flow is provided by Fleming's right-handed law.

Lenz's law is based on Faraday's import law. Faraday's law tells us that a flexible magnetic field will apply current to a conductor.

Lenz's law tells us the direction of what is currently being done, which contradicts the first ever-changing magnetic field it has produced. This is indicated in the Faraday law formula with the negative symbol (‘-’).

E = -\[\frac{d\Phi _{b}}{Bdt}\]

To find the direction of the induced field, the direction of the current and the polarity of the induced emf we apply the law of Lenz’s The term Flux is increasing too since the area enclosed is increasing. Motional emf also occurs if the magnetic field that moves and the rod or other object is stationary relative to the planet Earth or we can say some observer. We have also seen an example of this in the situation where a moving magnet induces an emf in a stationary coil. It is the relative motion that is important. What is emerging in these observations that we have already seen is a connection between magnetic and electric fields. A moving magnetic field generally produces an electric field seen through its induced emf. We already have seen in our article a moving electric field which generally produces a magnetic field moving charge that generally implies moving electric field and moving charge which produces a magnetic field.

Calculating Motional Electro-Motive Force

The emf of earth’s weak field magnetic is not ordinarily very large or we would notice voltage that along the rod of metal such as a screwdriver during ordinary motions. For example, we can say that a simple calculation of the motional emf of a 1 m rod that is moving at 3.0 m/s perpendicular to the planets earth’s field gives emf = Bℓv = (5.0 × 10⁻⁵ T)(1.0 m)(3.0 m/s) = 150 μV. 

We can say that there is a spectacular exception, however. In 1996 and 1992 attempts were made with the space shuttle to create large motions that have EMFs. A tethered Satellite which was to be let out on a length of 20 km of wire to create a 5 kV emf by moving at a speed orbital through the field of the planet Earth’s. To complete the circuit the stationary ionosphere was to supply a return path for the current to flow. The ionosphere is rarefied and we can say it is the partially ionized atmosphere at orbital altitudes. It could be said to conduct because of the ionization. The ionosphere that generally serves the same function as the stationary rails and the connecting resistor without which there would not be a complete circuit.

Concept Explanation

This concept of moving emf can be explained with the help of the Lorentz force concept that works on driver-free carriers. Let us consider any incorrect charge on the PQ conductor. As the rod moves at a constant speed v, the charging also travels at a constant speed v in front of the magnetic field B. Lorentz's power in this charge is given:

F = qvB

The work done to move the charge from P to Q can be provided by,

W = QBvl

As, emf is defined as the function performed per unit,

∈ = wq = Bvl