relation between magnetic permeability and magnetic susceptibility or prove that ur = 1 + X

 Prove that

Or

Q. Establish a relation between relative magnetic permeability and magnetic susceptibility of a material.

that is between

 and  

Ans:

1) Consider a magnetic material is placed inside a Solenoid.

2) Now the magnetic field inside the solenoid will increase. So new magnetic field is

B = B₀ + B_m

 

Where

&

Therefore

Where

B₀ =  is the magnetic field due to Solenoid

B_m = magnetic field due to the magnetic material

 

But we know that

Now putting the value of M, on 5.46 we get

 

 

 

Now we know that  

therefore

 

 

Where  

is called the relative magnetic permeability of the material.