(a) An iron ring of relative permeability \mu _{r} has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring.
(b) The susceptibility of a magnetic material is 0·9853. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

 

 
 
 
 
 

Answers (1)
S safeer

a) According to Ampere's circuital law, we have
 \oint B\cdot dl= \mu _{0}\mu _{r}I_{enclosed}
Here it is an iron ring
so field inside the ring is,
\oint B\cdot dl= B\int dl= B2\pi r
where 'r' is the radius of the ring.
Given that number of turns per meter = n
So

I_{enclosed}= 2\pi rn\, I
Therefore

B\cdot 2\pi r= \mu _{0}\mu _{r}\left ( 2\pi rn \right )I
B= \mu _{0}\mu _{r}nI
b)
  Given,
          susceptibility of a magnetic material = 0.9853
For paramagnetic material the value of susceptibility  X is . 0< X< \varepsilon
Where \varepsilon is a small positive number
Here X is 0.9853 very small number so it is a paramagnetic material.
When paramagnetic material placed in a uniform magnetic field the field gives concentrated lines inside the material.
    

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