The magnetic flux linked with a coil can be changed in many ways. For this,
( 1 ) the magnet can be moved with respect to the coil.
( 2 ) the coil can be rotated in the magnetic field.
( 3 ) the coil can be kept inside the magnetic field in proper manner and the magnitude of the magnetic induction can be changed.
( 4 ) the coil can be moved inside a non-uniform magnetic field.
( 5 ) the dimensions of the coil placed inside a magnetic field can somehow be changed.
“The induced emf. produced due to the change in magnetic flux linked with a coil due to some kind of motion is called motional emf.”
An example of motional emf. Is illustrated as under.
A U-shaped conducting wire is placed in a
plane perpendicular to the magnetic field. The magnetic field lines enter the plane of paper as shown by ( + ) sign.
A conducting rod is slid over the two arms of
the conductor with a constant velocity v. The
perpendicular distance between the two arms
of the conductor is l.
MN is the position of the rod at time t when the magnetic flux linked with the loop PMNO is
Flux = = ( area of PMNO ) ´ B ( magnetic field intensity )
= l B x, where x = PM = ON
As the emf. Is generated due to the motion of the rod, it is known as motional emf. Motional emf. Is produced by a conducting rod moving in a magnetic field in appropriate manner even without the U-shaped conductor. This is explained in the following example with the reason behind the origin of induced emf.
The reason behind the origin of induced emf
With the conducting rod moving with velocity v , positive ions and electrons in it also move perpendicularly to the magnetic field B . Electrons move from Q to P under the effect of Lorentz force
F = q v * B leaving positive ions exposed at Q. Thus rod behaves as a battery of emf B v l.
Conversion of Mechanical Energy into Electrical Energy
In the above example, let I be the current flowing through the sliding conductor. As it is moving in a magnetic field entering the plane of paper, conventional current flows in the rod from P to Q and the rod experiences force I B l in the direction opposite to its velocity v. Thus to maintain its uniform velocity, a force of magnitude I B l must be applied in the direction of its velocity. Such a force is called Lenz force.
Hence, mechanical power, Pm = force ´ velocity = Fv = B I l v
and electrical power, Pe = voltage ´ current = B v l * I = B I l v
Thus, mechanical power spent is converted into electrical power. Here ideal case of zero circuit resistance is considered.
( 1 ) the magnet can be moved with respect to the coil.
( 2 ) the coil can be rotated in the magnetic field.
( 3 ) the coil can be kept inside the magnetic field in proper manner and the magnitude of the magnetic induction can be changed.
( 4 ) the coil can be moved inside a non-uniform magnetic field.
( 5 ) the dimensions of the coil placed inside a magnetic field can somehow be changed.
“The induced emf. produced due to the change in magnetic flux linked with a coil due to some kind of motion is called motional emf.”
An example of motional emf. Is illustrated as under.
A U-shaped conducting wire is placed in aplane perpendicular to the magnetic field. The magnetic field lines enter the plane of paper as shown by ( + ) sign.
A conducting rod is slid over the two arms of
the conductor with a constant velocity v. The
perpendicular distance between the two arms
of the conductor is l.
MN is the position of the rod at time t when the magnetic flux linked with the loop PMNO is
Flux = = ( area of PMNO ) ´ B ( magnetic field intensity )= l B x, where x = PM = ON
As the emf. Is generated due to the motion of the rod, it is known as motional emf. Motional emf. Is produced by a conducting rod moving in a magnetic field in appropriate manner even without the U-shaped conductor. This is explained in the following example with the reason behind the origin of induced emf.
The reason behind the origin of induced emf
With the conducting rod moving with velocity v , positive ions and electrons in it also move perpendicularly to the magnetic field B . Electrons move from Q to P under the effect of Lorentz force
F = q v * B leaving positive ions exposed at Q. Thus rod behaves as a battery of emf B v l.
Conversion of Mechanical Energy into Electrical Energy
In the above example, let I be the current flowing through the sliding conductor. As it is moving in a magnetic field entering the plane of paper, conventional current flows in the rod from P to Q and the rod experiences force I B l in the direction opposite to its velocity v. Thus to maintain its uniform velocity, a force of magnitude I B l must be applied in the direction of its velocity. Such a force is called Lenz force.
Hence, mechanical power, Pm = force ´ velocity = Fv = B I l v
and electrical power, Pe = voltage ´ current = B v l * I = B I l v
Thus, mechanical power spent is converted into electrical power. Here ideal case of zero circuit resistance is considered.
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