A tightly-wound, long solenoid having 50 turns `cm^(-1)`, carris 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`
`= 50 xx 100^2 m^(-1) xx 4A = 2 xx 10^4 A m^(-1)`
The magnetic field `B = mu_0 H`
`= 4pi xx 10^(-7) Tm A^(-1) xx 2 xx 10^4) A m^(-1)`
= 8pi xx 10^(-3) T= 25 mt`.
The value of `H` does not change as the iron core is inserted and remains `2 xx 10^4 A m^(-1)`. The magnetic field `B` becomes
`B = mu_0 (H+I)`.
`= (4pi xx 10^(-7) Tm A^(-1)) (2 xx 10^4 xx 10^6) A m^(-1) = 5.05 T`.
It should be noted that the magnetic intensity `H` is very small as compared to the magnetization `I` in presence of the iron core.