Physics Times 07.2019

Electromagnetic Induction

1.Magnetic Flux()
The magnetic flux through a small surface of area

dA is d B dA 

 



(^) B

-magnetic field,
dA


• area vector defined normal to the surface.
  Flux through a large surface is

   B dA B A B(if

   

 is uniform)

SI units: Tesla/meter^2 or weber(Wb)

2. Faraday’s laws of electromagnetic
   induction
   (I) Induced E.M.F

 



    

d d

e N N

dt dt

(II) Induced Current

    

  

I e N d

R R dt

(III) Induced Charge

1

ind

d d

dq i dt dt

R dt R

      

  

 

q

R

 

3. Lenz's Law
    The direction of the induced emf is always such
   that it tends to oppose the change in magnetic flux
   that has caused it.


4. Motional EMF
   The induced emf due to the motion of electric
   conductor in the presence of magnetic field is called
   as motional emf. Motional emf can arise either by
   translation or rotation of a conductor.


5. Motional emf due to translation
   Consider a conductor, moving with a velocity

v, in a magnetic field B


.
The general expression for motional EMF across
the ends of a rod having irregular shape as
shown in the figure is  V Bl v' '

Where l' is effective length which is equal to

the shortest distance between the two end points

P and Q.

v'- Component of velocity perpendicular to l'

B - External magnetic field which is perpendicular

to both v' and l'

6. Motional emf due to rotation
   Consider a conducting rod rotating with angular
   velocity  about an axis passing through one of
   its ends. The length of the rod is l.
   The general expression for motional EMF across
   the ends of a rod which is in rotation about P.

'2

1

2

  V B l

l' is the effective length of the rod.

7. Induced EMF in a sliding Conductor
   Consider a conducting rod of length l that moves
   on a U-shaped loop. An external force acts on the
   rod to move it with velocity v.

(I)Induced current

Induced current



in 

Bvl

i

R R

(II) Magnetic force on the conductor

 ^22

    

in  

F Bi l B Bvl l B vl

R R

(III) Power dissipiated in moving the conductor

2 2 2

 . 

 

agent agent

P dW F v B v l

dt R

(IV) Electrical power

Electromagnetic Induction

1.Magnetic Flux( )




2. Faraday’s laws of electromagnetic
   induction


3. Lenz's Law
   


4. Motional EMF


5. Motional emf due to translation
   





6. Motional emf due to rotation
   



7. Induced EMF in a sliding Conductor

(^2) 2 2 2
2
thermal
P i R Bvl R B v l
R R
   
  

23. Electro Magnetic Induction