Motional emf, Electromotive Force, Induced emf
We all know that when an electrical conductor is introduced into a magnetic
field, due to its dynamic interaction with the magnetic field, emf is
induced in it. This emf is known as induced emf. In this article, we will
learn about motional emf where emf is induced in a moving electric
conductor
in the presence of a magnetic field.



Proof of motional emf
	 
	Motional EMF

	
Consider a straight conductor PQ as shown in the figure, moving in the
rectangular loop PQRS in a uniform and time-independent magnetic field B,
perpendicular to the plane of the system.
	
Let us suppose the motion of rod to be uniform at a constant velocity of v
m/sec and the surface to be frictionless.
	
Thus, the rectangle PQRS forms a closed circuit enclosing a varying area
due to the motion of the rod PQ.
	
The magnetic flux ΦB enclosed by the loop PQRS can be given as
ΦB = Blx


Where, RQ = x and RS = l, Since the conductor is moving, x is changing with time.
Thus, the rate of change of flux ΦB will induce an emf, which is given by:
 \begin{array}{l}\epsilon =\frac{-d\phi _{B}}{dt}=\frac{
-d}{dt}(Blx)\end{array} 

Where, the speed of conductor (PQ), v = -dx/dt and is the formula of induced
emf. This induced emf due to the motion of an electric conductor in the presence
of the magnetic field is called motional emf. Thus, emf can be induced in two
major ways:

 
Due to the motion of a conductor in the presence of a magnetic field.
 
Due to the change in the magnetic flux enclosed by the circuit.


Following is the table of links related to EMF:

Electromotive Force
Current Electricity


This concept of motional emf can be explained with the help of the concept of
Lorentz force acting on free charge carriers of the conductor. Let us consider
any arbitrary charge q in the conductor PQ. As the rod moves with a constant
speed v, the charge is also moving with a speed v in the presence of magnetic
field B. The Lorentz force on this charge is given by:
	F = qvB

The work done in moving the charge from P to Q can be given by,
	W = QBvl

Since, emf is defined as the work done per unit charge,
	∈ = wq=Bvl



Frequently Asked Questions – FAQs

 
Q1 What is meant by electric potential?
Electric potential is the quantity of work required to displace a unit charge 
from a reference point to a specific point against an electric field.
 
Q2 What is the full form of emf?
Electromotive force is the full form of emf.
 
Q3 What is electromotive force?
Electromotive force or emf is equal to the potential terminal variation when no
electric current flows.
 
Q4 What is induced emf?
Induced emf is the generation of a potential difference in a coil due to the
changes in the magnetic flux through it.
 
Q5 What is motional emf?
Motional emf is the emf induced by the movement of the conductor through the
magnetic field.
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Induced Electromotive Force and Current



What is an Induced Electromotive Force?

 
We can induce a current in the loop by changing the magnetic field. As we
have discussed earlier in Faraday’s law, we have seen some experiments based on
this theory.
 
In the first experiment, the ammeter shows zero current reading which proves
that a stationary magnet does not induce a current in a coil.
 
In the second experiment, the meter shows the induction of the current which
demonstrates that it is due to the change in the magnetic field as the magnet is
moved towards or away from the coil.
 
So it is clear that a constant magnetic field does nothing to the coil,
while a changing field causes current to flow.
 
Hence, we have observed from the above experiments that, only a changing
magnetic field can make the current flow. To be more accurate, if the magnetic
flux through a coil is changed, a voltage will be produced. This voltage is
known as the induced emf.



What is Magnetic Flux?

 
Magnetic flux is linked with the surface area when it is held inside the
magnetic field. When the direction of the magnetic field is perpendicular to the
surface area, magnetic flux on the surface is more. When the magnetic field is
parallel to the surface area, the magnetic flux on the surface is less.
 
The unit of magnetic flux is Weber (Wb).


Have you ever wondered that when the coil completely remains inside the
magnetic field during motion, why no current flows through it?

When the coil is entirely inside the magnetic field, the two ends of the
coil become positive and the other ends of the coil become negative. The
potential difference of the coil will be equal in each case. So when two
cells having equivalent electromotive force are connected to each other,
then no current flows through the coil, and no net Induced Electromotive
force exists in the coil.

Do you know what happens when the string of the electric guitar vibrates?
When the string of an electric guitar vibrates, an electromotive force is
introduced in the coil. The induced magnetization in the string is picked
up
from the vibration of the guitar. The input of an amplifier of the guitar
is
connected to the two ends of the coil which are connected to the speakers.



Frequently Asked Questions – FAQs




Q1

What is a force?
A force is usually defined as an influence that can alter the motion of a
body. A force can cause a body with mass to alter its velocity.
Q2

What is a magnetic field?
A magnetic field is a field that describes the magnetic effect on moving
charges, magnetic materials and electric currents.
Q3

Explain the force due to a magnetic field.
Magnetic fields can exert a force on an electric charge only if it is
moving, just as a moving charge generates a magnetic field. This force
increases with both an increase in charge and magnetic field strength. In
fact, the force is greater when charges have higher velocities.
Q4

What is meant by magnetic flux?
Magnetic flux is the number of magnetic field lines existing on a given
closed surface.
Q5

What is meant by electromotive force?
In electromagnetism, an electromotive force is an electrical force
generated
by a non-electrical source. It is calculated in volts. 


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Magnetic Field
The magnetic field is the area around a magnet in which the effect of
magnetism is felt. We use the magnetic field as a tool to describe how the
magnetic force is distributed in the space around and within something
magnetic in nature. In this article, let us familiarise ourselves with the
magnetic field, magnetic field intensity, and its characteristics.



What is a Magnetic Field?

 Magnetic Field is the region around a magnetic material or a moving
electric charge within which the force of magnetism acts.

	 
	Magnetic Field
A pictorial representation of the magnetic field which describes how a
magnetic force is distributed within and around a magnetic material

A magnetic field is a vector field in the neighbourhood of a magnet,
electric current, or changing electric field in which magnetic forces are
observable. A magnetic field is produced by moving electric charges and
intrinsic magnetic moments of elementary particles associated with a
fundamental quantum property known as spin. Magnetic field and electric
field are both interrelated and are components of the electromagnetic
force,
one of the four fundamental forces of nature.





Symbol
B or H
Unit
Tesla
Base Unit
(Newton.Second)/Coulomb




History of Magnetic Field

The research on the magnetic field began in 1269 when French scholar Petrus
Peregrinus de Maricourt mapped out the magnetic field on the surface of a
spherical magnet using iron needles. He noticed that the resulting field lines
crossed at two points. He named these points “poles.” After this observation, he
stated that magnets always have North and South poles irrespective of how finely
one slices them.
Three centuries later, William Gilbert stated that Earth is a magnet.
In 1750 John Mitchell, an English clergyman and philosopher, stated that
magnetic poles attract and repel each other.
In 1785, Charles-Augustin de Coulomb experimentally verified Earth’s
magnetic field. In the 19th century, French mathematician and geometer Simeon
Denis Poisson created the first model of the magnetic field, which he presented
in 1824.
By the 19th century, further revelations refined and challenged 
previously-held notions.
In 1819, Danish physicist and chemist Hans Christian Oersted discovered that
an electric current creates a magnetic field around it.
In 1825, André-Marie Ampère proposed a model of magnetism where this force
was due to perpetually flowing loops of current, instead of the dipoles of
magnetic charge.
In 1831, English scientist Faraday showed that a changing magnetic field
generates an electric field. In effect, he discovered electromagnetic induction.
Between 1861 and 1865, James Clerk Maxwell published theories on electricity
and magnetism. It was known as Maxwell’s equation. These equations describe the
relationship between electricity and magnetism.



Illustration of Magnetic Field
Typically, a magnetic field can be illustrated in two different ways.
Magnetic Field Vector
Magnetic Field Lines



Magnetic Field Vector

The magnetic field can be mathematically described as a vector field. The vector
field is a set of many vectors that are drawn on a grid. In this case, each
vector points in the direction that a compass would point and has a length
dependent on the strength of the magnetic force.
	 
	Vector Field of a Bar Magnet



Magnetic Field Lines
Field lines is an alternative way to represent the information contained
within a magnetic vector field. Magnetic field lines are imaginary lines.

Magnetic field lines are a visual tool used to represent magnetic fields.
They describe the direction of the magnetic force on a north monopole at any
given position

The density of the lines indicates the magnitude of the field. Taking an
instance, the magnetic field is stronger and crowded near the poles of a
magnet. As we move away from the poles, it is weak, and the lines become
less dense. Inverse square law

	Magnetic Field Lines for Bar Magnet
	 
	The figure shows a magnetic field lines plot for a bar magnet



Properties of Magnetic Field Lines

Magnetic field lines never cross each other
The density of the field lines indicates the strength of the field
Magnetic field lines always make closed loops
Magnetic field lines always emerge or start from the north pole and
terminate at the south pole.




Magnetic Field Intensity
Magnetic field strength is also magnetic field intensity or magnetic intensity.
It is represented as vector H and is defined as the ratio of the MMF needed to
create a certain Flux Density (B) within a particular material per unit length
of that material. Magnetic field intensity is measured in units of amperes/meter.
It is given by the formula:
	H = B/μ - M
Where,

B is the magnetic flux density
M is the magnetization
μ is the magnetic permeability


The SI unit of magnetic field intensity is Tesla. One tesla (1 T) is defined
as the field intensity generating one newton of force per ampere of current
per metre of conductor.



How does a Magnetic Field Originate?
The magnetic field arises when a charge is in motion. There are two basic ways
to arrange for a charge to be in motion and generate a useful magnetic field. 
Following are the two ways:



Magnetic Field created by a Current-Carrying Conductor
Ampere suggested that a magnetic field is produced whenever an electrical
charge is in motion. For our understanding, let us consider a wire through
which the current is made to flow by connecting it to a battery. As the
current through the conductor increases, the magnetic field increases
proportionally. When we move further away from the wire, the magnetic field
decreases with the distance. Ampere’s law describes this. According to the
law, the equation gives the magnetic field at a distance r from a long
current-carrying conductor I.
	B = µ0I / 2πr

In the equation, µ0 is a special constant known as the permeability of free
space(µ0=4π×10-7 T⋅ m/A).

Materials with higher permeability possess the ability to concentrate on 
magnetic fields.

The magnetic field has direction as it is a vector quantity. For
conventional current flowing through a straight wire, this can be found by
the right-hand rule. Imagine gripping your right hand around the wire with
your thumb pointing in the current direction to use this rule. The fingers
show the direction of the magnetic field, which wraps around the wire.
Watch the Video and Learn about Magnetic Field Due to Solenoid and
Properties of Magnetic Field Lines 1,158



Motion of Electrons around the Nuclei of Atoms
Permanent magnets work based on the motion of electrons around the nuclei.  We
have observed that only some materials can be made into magnets, and some much
stronger than others. To attain this state, some specific conditions should be
met:

Atoms have many electrons, and they are paired in such a way that the
overall magnetic field cancels out. Two electrons paired this way are said to
have opposite spins. From this, we understand that if we want a material to be
magnetic, we need to have atoms that have one or more unpaired electrons with
the same spin. Iron is a material that has four such electrons and therefore is
good for making magnets out of it.
A tiny piece of material consists of billions of atoms. If they are oriented
randomly, the overall field cancels out, regardless of how many unpaired
electrons the material has. The material has to be stable enough at room
temperature to allow an overall preferred orientation to be established. If
established permanently, then we have a permanent magnet, also known as a
ferromagnet.
Some materials become sufficiently well-ordered to be magnetic when in the
presence of an external magnetic field. In the external field lines, all the
electron spins up, but the alignment vanishes once the external field is 
removed. These kinds of materials are known as paramagnetic.




Frequently Asked Questions – FAQs





Q1

Why are magnetic flux lines important?
Magnetic flux lines are important because of the following reasons:

Magnetic field lines are the lines in a magnetic field the tangent of which
at any point will give the field direction at that point and its density
gives the magnitude of the field.
The magnetic field intensity depends on the number of magnetic field lines.
The lines are higher at the poles, that is why the magnetic field at the
poles is stronger.
The strength of a magnetic field is dependent on the number of magnetic
field lines at a particular area of consideration.


Q2

What causes the Earth’s magnetic field?
The Earth’s magnetic field is generated deep down the Earth’s core. The flow of
liquid iron at the centre of the Earth generates an electric current that 
produces magnetic fields. Charged metals passing through these fields create 
electric currents of their own, so the cycle continues. This self-sustaining
loop is known as the geodynamo. The spiralling caused by the Coriolis force 
aligns separate magnetic fields in the same direction. The combined effect of 
magnetic fields produces one vast magnetic field engulfing the planet.

Q3

What is magnetic field?
Magnetic Field is the region around a magnetic material or a moving electric
charge within which the force of magnetism acts.

Q4

Define magnetic flux density.
Magnetic flux density is the amount of magnetic flux in an area taken
perpendicular to the magnetic flux’s direction. It is denoted by the symbol B
and it is measured in the units of Tesla.

Q5

Define magnetic field intensity.
The Magnetic Field Intensity or Magnetic Field Strength is a ratio of the MMF
needed to create a certain flux density (B) within a particular material per 
unit length of that material.

Q6

Are there magnetic fields in space?
Yes, there are magnetic fields in space. The spiral arms of the Milky Way seem
to have some very large-scale organised magnetic field on the basis of studies 
of large numbers of pulsars and the polarisation of their radio signals. 
Interstellar dust clouds have been found to have magnetic fields.  As these 
clouds collapse, the fields are amplified

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