The number of turns of a solenoid of length 10 cm is 1000 . If the air inside it is replaced by a magnetic material and 1 A current is passed through the coil , the magnitude 20 T . . Determine the magnetic intensity at that point and relative magnetic permeability of the magnetic permeability of the material .

Explanation

Number of turns per unit length of the coil ,
`n=(1000)/(10)=100"cm"^(-1)=10000m^(-1)`
`therefore` Magnetic intensity on the axis ,
`H=nI=10000xx1=10000A.m^(-1)`
If the interior of the solenoid is vacuum or contains air then magnetic field on the axis ,
`B_(0)=mu_(0)nI=(4pixx10^(-7))xx10000=12.56xx10^(-3)T`
Due to the presence of the magnetic material
`B=munI=20T`
`therefore` Relative magnetic permeability ,
`mu_(r)=(mu)/(mu_(0))=(B)/(B_(0))=(20)/(12.56xx1010^(-3))=1592`