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Motional Electromotive force(IV) is considered one the most difficult concept.
Motional Electromotive force(I), Motional Electromotive force(II), Energy consideration in Motional Emf, Motional Electromotive force(III) is considered one of the most asked concept.
68 Questions around this concept.
A rectangular loop has a sliding connector PQ of length and resistance
and it is moving with a speed
as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents
are
A conducting square loop of side L and resistance R moves in its plane with a uniform velocity perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure.
The induced emf is
A wire of length moving with velocity
at right angles to a magnetic field of
. The magnitude of induced emf, between the ends of the wire will be :
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An emf of is induced in a metal rod of length
held normal to a uniform magnetic field of
, when moves with a velocity of:
A boat is moving due east in a region where the earth’s magnetic field is 5.0 × 10-5 N A-1 m-1 due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is 1.50 m s-1, the magnitude of the induced emf in the wire of the aerial is
A metallic rod of length 'I' is tied to a string of length 2I and made to rotate with angular speed on a horizontal table with one end of the string fixed.If there is a vertical magnetic field 'B' in the region,the e.m.f. induced across the ends of the rod is :
In an AC generator, a coil with N turns, all of the same area A and total resistance R , rotates with frequency in a magnetic field B . The maximum value of emf generated in the coil is
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If a conducting rod of length is moving with a uniform velocity
perpendicular to the region of the uniform magnetic field (
) which directed into the plane of the paper as shown in the below figure.
Then the magnetic force on +ve charges is given by toward side b.
And similarly the magnetic force on -ve charges is given by toward side a.
So positive and negative charges will accommodate at side b and side a respectively. This will create an electric field having direction from b to a. And electric force due to this field on charges will be given as
Applying Equilibrium condition between electric and magnetic force
So Potential difference induced between endpoints of the rod is given by
this Potential difference () is known as motional emf.
So Motional EMF is given by
where
magnetic field
length of conducting
the velocity of rod perpendicular to a uniform magnetic field.
If conducting PQ rod moves on two parallel conducting rails as shown in below figure
and we wanted to find motional emf of the moving rod
Method I-
As magnetic flux is given by
So initial flux passing through PQRS is given by
And when rod starts moving this flux will change then the change in flux ix given as
So the motional emf is given as
Method II-
Due to the motion of the rod +ve and -ve charges of the rod will start to move towards point Q and P respectively.
Then the magnetic force on +ve charges is given by toward Q.
And similarly, the magnetic force on -ve charges is given by toward P.
So the work done by the magnetic force to move the +ve charge from P to Q is given by
So potential difference across PQ is given as
So the motional emf is given as
As we learn for the above figure Motional EMF is given by
where
magnetic field
length of conducting
the velocity of rod perpendicular to a uniform magnetic field.
So now we want to find whether the law of conservation is applicable for the motional emf or not?
So Induced Current in the conducting rod is given as
where r is the resistance of the rod
And assuming resistance of other arms (i.e PS,SR,RQ) is negligible.
Magnetic force on conducting rod is given as
The power dissipated in moving the conducting rod -
Electric Power or the rate of heat dissipation across the resistance is given as
Since So we can say that the principle of conservation of energy is applicable for the motional emf.
General Case-
Motional emf when are at some angle with each other as shown in the below figure.
For example-
then Induced emf
Motional E.m.f due to rotational motion-
If a conducting rod PQ is rotating with angular velocity about its one end (Q) in a uniform magnetic field as shown in the below figure.
then
where
Similarly
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