SELF INDUCTANCE

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                Self inductance

It is the phenomenon of Producing induce emf in a coil when a changing current flows through it. 





Coefficient of self inductamce (induction) 


The flux linked with coil is directly proportional to the changing current passing through it. 

If  magnetic flux and I be the current for a given coil then, 

                Magnetic flux is directly proportional to the current. 

Magnetic flux = LI
Where, L = coefficient of self inductance (induction) 

W. K. T
 Acc to faraday law

E = - d(magnetic flux) /dt

E = - LdI/dt

L = - E/(dI/dt) 

Self inductance unit = volt/(ampere/sec) 

S. I unit of self inductance is henry(H). 


Self induction for a long solenoid




Area of cross section = A
N = no. Of turns in solenoid
n = no. Of turns per unit length

      n = N/l

     N = nl
W. K. T

 M. F inside the solenoid
    B = uo × nI
Where uo = permeability of the material

 Now, flux linked with each turn of solenoid
   Magnetic flux = BA
   Magnetic flux = uonIA

Now, flux linked with entire solenoid
 = flux linked with each turn × total no. Of turns 

Flux linked with entire solenoid = uo × nIA × N

Flux linked with entire solenoid = uo × nIA × nl       ........ (1) 

W. K. T

Flux linked with entire solenoid = LI    ...... (2) 

On comparing (1) and (2) 

LI = uo nIAnl
L = uo nAnl

L = uo NANl/l×l

L = uo NAN/l


The factors on which self inductance depends
(1) L is directly proportional to N×N
(2) L is directly proportional to A

(3) permeability of core material

      Self inductance is directly proportional to the permeability of the material filled inside the solenoid. 

For ex    the self inductance of air filled solenoid is less than the self inductance of a soft iron filled solenoid. 
Because the permeability of the soft iron is greater than air. 

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