MUTUAL INDUCTANCE

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             Mutual inductance

It is the phenomenon of producing induced emf in one coil due to a change of current in the neighbouring coil. 


Coefficient of mutual induction


It is shows that the flux linked with secondary coil is directly proportional to the current in the primary coil. 

Flux on the secondary coil is directly proportional  to the current in primary coil. 

So, 

Flux on secondary coil = M × Ip
Where, M = coefficient of mutual inductance
              Ip = current in primary coil

W. K. T
 Acc to faraday law
E = -d(flux) /dt

E = - d(M Ip) /dt

E = - M dIp/dt

M = - E/(dIp/dt) 

Unit = volt sec/ ampere

SI unit = henry

Mutual induction for two co axial solenoid




l = length of solenoids
N1 and N2 = total no. Of turns in 1 and 2 solenoid

n1 and n2 = no. Of turns per unit length in 1 and 2 solenoid

n1 = N1/l  ,   n2 = N2/l

r1 and r2 = radius of cross section of solenoid and (r1 is greater than r2)

Area = πr×r = area of cross section of inner Solenoid. 

So first, assumes that I2 current flows through solenoid 2

M. F sets up inside the solenoid 2 given as

   B2 = uo n2 I2
Now, magnetic flux linked with each turns of solenoid 1.

Flux on solenoid 1 = B2A

Now, the total magnetic flux linked with entire solenoid 1
        = B2 A N1
        = uo n2 I2 A N1     ........ (1) 

W. K. T

Total magnetic flux linked with entire solenoid 1 = M1 I2     .... (2) 

On comp. (1) and (2) 

M1 I2 = uo n2 I2 A N1

M1 = uo n2 A N1
          Or 
M1 = uo n2 A n1 l

M1 = uo ( N1/l) × A × N2 × l / l

M1 = uo N1 N2 A / l
          Or 
M2 = uo N1 N2 A / l
Where, M1 = mutual inductance of coil 1 with respect to 2
    M2 = mutual inductance of coil 2 with respect to 1
Clearly,     M1 = M2
If a medium of relative permeability ur is present within the solenoids, then
M = ur uo n1 n2 A l

 Factors on which mutual induction depends 


(1).  M is directly proportional to N1 N2
(2).  M is directly proportional to common area of the solenoid 
(3). M is inversely proportional to the relative separation between solenoid
     


Mutual induction for arrangement 1 is greater then arrangement 2

(4). M is depends on the orientation between solenoid. 

M is max. When both solenoid wound over one other. 

M is min. When solenoid are perpendicular to each other. 





(5). M is depends on the permeability of the core material filled inside the solenoid.

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