6. Class 12th Physics | EMF Induced in a Moving Conductor in Uniform Magnetic Field-Motional EMF

6. Class 12th Physics | EMF Induced in a Moving Conductor in Uniform Magnetic Field-Motional EMF


let us study about e m f induced in a moving
conductor in uniform magnetic field. here we can see this is the uniform magnetic field
induction b vector, in which a conductor of length l is translating with a speed v. now
in this situation we can say that as conductor is moving with a speed v, within the conductor
each free electron also moves with a speed v, and we can say, each free electron, of
conductor, experiences a magnetic force. and this magnetic force can be given as if we
write force on each free electron as f e, it is e v b because, the electron is moving
with a speed v perpendicular to the magnetic field. now in this situation the direction
of this magnetic force by right hand palm rule we can say as being a negative charge
it’ll be in downward direction. so we can say, due to this magnetic force, we can write
here free electrons, will drift, towards q, the end q of the rod, so this’ll be slightly
negative and as electrons are shifted from point p it’ll become slightly positive.
and due to these charges occurring, by the drift of these electrons, an electric field
is established in the conductor in downward direction which can be written as an induced
electric field. and due to this induced electric field if we talk about this electron, in downward
direction it is experiencing a magnetic force e v b. and due to drift of electrons, an induced
electric field is developed which applies an upward force e e i on the electron. so
we can directly write, due to this magnetic force, free electrons will drift towards q,
and this induces, an electric field e i, within the conductor, as we’ve just now discussed.
and here we can say in steady state, steady state implies that this electric field will
increase continuously, due to the drift of electrons till this electric force will balance
the magnetic force on electron. so no more drifting will take place. so in this situation
in steady state e e i will be equal to e v b. and this gives us the value of induced
electric field that is v b, which is a constant within the volume of this conductor. and due
to this electric field we can say, a potential difference is also induced across the ends
p and q. so here we can write, the potential difference, across the rod, due to e i is,
this can be written as v p minus v q and this we can simply write as e i multiplied by l,
as e i is constant. whenever electric field is constant in a region potential difference
can be calculated by product of, magnitude of field and the seperation between the points.
so here, this can be written as, b, v, l. and 1 important point here is, this potential
difference is induced, without any electrostatic cause, that is just because of magnetic force.
so we can term this potential difference as an electromotive force. so here we can write
it as an induced e m f, electro motive force due to, motion of a conductor, in magnetic
field, it is denoted by small e, across the ends, which can be given as b v l. this is
a very useful relation and as it is due to motion of a conductor, it is also termed as
a motional e m f. and this also forms, a strong basis of many different kind of problems,
which are based on conductor motion in a magnetic field. we’ll continue on the next sheet,
by getting the same motional e m f by using faraday’s law also.
in continuation let’s discuss the explanation of motional e m f by using faraday’s law.
we already studied in the faraday’s law that whenever there is a relative motion between
a conductor and magnetic field, such that a conductor cuts magnetic lines, then e m
f induced in the conductor can be given by, rate of change or rate of cutting the magnetic
flux. here we can see as magnetic induction is b, and the conductor is translating with
speed v, we can say in time d t it’ll travel a distance v d t and reach this position.
and in this time d t we can say this is the area swept by the conductor. so we can directly
calculate, the flux, magnetic flux, cut by conductor, in time d t is, d phi, and this
d phi we can write as, b dot d s, which is the area in which we wish to find the magnetic
flux. this’ll be b multiplied by, here the area can be directly given as l v d t. if
this is the magnetic flux by faraday’s law we can say e m f induced, in conductor is,
this can be given as e is mod of d phi by d t. and d phi by d t here we can directly
see it is given as b v l, which is the motional e m f we’ve already derived by using induced
electric field. and here the direction of, induced e m f, can be directly given by, right
hand palm rule. here right hand palm rule can be directly applied by placing, fingers
along the direction of b vector, thumb along the direction of velocity vector. and in this
situation, the palm face will point, toward the high potential end of the conductor. like
in this situation if i use my right hand fingers inward and, thumb along the direction of velocity,
my palm face is pointing toward p. and point p can be taken as high potential and the end
can be marked as positive, and the low potential end q can be marked as, negative.

34 Replies to “6. Class 12th Physics | EMF Induced in a Moving Conductor in Uniform Magnetic Field-Motional EMF”

  1. Sir in the motional emf video wont the rod follow lens law
    Current should flow from top to bottom.
    Please help sir????

  2. sir i want to purchase your study material for physics . for 11th and 12th from where should i purchase it?

  3. sir at the instant when the rod starts to move (i.e t=o) their wont be any potential difference between the ends of the rod ,isnt it sir?

  4. sir we define emi for a loop of wire or a coil but in this case there is no loop present?? when we move the conductor from position 1 to 2 in a constant and uniform magnetic field the area and the field lines passing normally through the area of conductor is not changing so how can we use this method to calculate the EMF??

  5. Sir but why will emf be generated..both the electric field cancel each other…?? And if we try to do the the above discussion with faraday' is law…how can we justify….???

  6. Sir
    Good Evening
    I think the direction of drifting of electrons in this video is wrong. According to Flaming's left hand rule the electrons will go in the upward direction.
    Yours Faithfully
    Ujjawal Rathore

  7. Sir when velocity is perpendicular to magnetic field the particle moves in circular motion and if we are considering the motion of individual electron then it's path should also be circular. Then why are the electrons drifting in the bottom of rod?
    And in this case the magnetic force will do work. which will change the velocity of electrons. and we know that work done in magnetic field by magnetic forces is always zero which here is violated.
    Kindly answer my query.

  8. sir in the last few minutes of explanation you concluded that point p is high potenial end and q is at low poten. then induce current will flow in direction from p to q.but by right hand fleming rule i am getting direction of current from q to p. please correct me if i am going
    wrong

  9. sir you said that that the potential diff is caused due to no no electrostatic causes and is due to a magnetic force….so why did you term it as the EMF?? i didnt understand the reason

  10. Sir due to magnetic force electron was tending to move downward which means higher potential must be at downward then why u have take higher potential at upward end of the rod

  11. sir why emf is being produced as i feel there is no change in magnetic flux ( no change in magnitude of MF, area of conductor , orientstion of conductor ) ? Sir please tell what are the parameters which are changing which are producing the induced current in conductor.

  12. sir Magnetic field is const and conductor is not forming any loop so change in Magnetic flux should be ZERO.

  13. Sir if velocity is constant then area swapped by conductor in time dt will be same after some time.so change in magnetic flux will not change .therefore emf will be induced but only for initial time. Am I correct.

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