Figure shows a solenoid current of

I- ampere Its area is 'A' and number of turns n.
a. What is the flux density of the solenoid field inside ?
b. If magnetic material in the form of a rod of area 'a' `(a lt lt A)` is inserted into the solenoid, what is the magnetising field strength ?
c. Find the total flux density inside the specimen.

Explanation

a. `B_0=mu_0nI` (taking n number ber turns/unit length )
b. H = nI
c. `B=B_0+B_m` Total flux density B. Total flux density free space `=B_0`
`B_m` - induction due to magnetisation of material.
d. Susceptibility , `X_m=I/H`
`muH=mu_0H+mu_0I " ":.mu=mu(I+I/H)=mu_0(I+X_m)`
c. `B=B_0+B_m` Total flux density B. Total flux density free space `B_0`
`B_m` - induction due to magnetisation of material .
d. Susceptibility ,`X_m=I/H`
`muH=mu_0H+mu_0I" ":.mu=mu_0(1+I/H)=mu_0(I+X_m)`
Let `mu_r` be the relative permeability , then `mu_rmu_0=mu_0(I+X)" ":.mu_r=(I+X)`
e. Diamagnetic `-1lexlt0,0lemu_rlt1,multmu_0`
Paramagnetic `0ltxlt,mu_rgt1,mugtmu_0`
Ferromagnetic `X gtgt1,mu_rgtgt1,mugtgtmu_0`
Examples : diamagnetic - Bismuth , lead , gold , mercury , silver etc.
Paramagnetic - Aluminium , chromium , oxygen etc.
Ferromagnetic - Aluminium , chromium, oxygen etc.