# 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”

Sir in the motional emf video wont the rod follow lens law

Current should flow from top to bottom.

Please help sir????

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

thanks a lot sir i was fed up with physics I had given up ur video s are too good n sufficient thanks

sir why the electric field applies the force in upward direction as the dir of electric field is in downward

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?

sir, how will drift of electrons generate electric field…?

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??

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….???

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

Sir i am a NEET aspirant in class 12

Which book should i follow ??

Please why you take the mode defy over dety ?

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.

sir ……how to use flemmings left hand rule here???? instead of right hand palm rule

Sir plz tell me Vp-Vq=EL how it comes i didnt remmber it plz help

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

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

sir, will the emf be induced in an open circuit ( such as an open loop) if the flux through that loop is changing

Sir, you are really great!

May i know the name of the pen being used in this video?

sir, at 1:25 you took the force on electron downwards, but sir the force will be in upward direction.

Thanx for making my potential diff. Concept clear

Thank you very much. This explanation helped my understanding of motional emf.

Sir what is meaning of electrostatic cause?

u should have mentioned current direction rather than electrons

i was nice though :))

Excellent

Sir can u explain how u use right hand palm rule in this …

Sir why is our palm face (in right hand palm rule) towards high potential instead of low potential ??

You are a true genius god bless you sir

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

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.

I think sir , In video no 3 of emi polarity in 2. And 3 example is wrong

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

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.

Sir +I've sign is considered as a higher potential or negative sign