A tightly-wound, long solenoid having 50 turns `cm^(-1)`, carries a current of `4.00 A`. Find the magnetic intensity `H` and the magnetic field `B` at the centre of the solenoid. What will be the values of these quantities if an iron core is inserted in the solenoid and the magnetization `I` in the core is `4.00 xx 10^6 A m^(-1)` ?

Explanation

The magnetic intensity H at the centre of a long solenoid is H = ni
`=50xx10^(2)m^(-1)xx4A=2xx10^(4)A//m`
The magnetic field `B = μ_(0)H`
`=4pixx10^(-7)T-m//Axx2xx10^(4)A//m`
`=8pixx10^(-3)T=25mT`
The value ofH does not change as the iron core is inserted and remains `2xx10^(4)A//m`. The magnetic field B becomes `B=mu_(0)(H+I)=(4pixx10^(-7)t-m//A)(2xx10^(4)+4xx10^(6))A//m=5.05T`
It should be noted that the magnetic intensity H is very small as compared to the magnetization I in presence of the iron core.