The magnetic field (B) inside a long solenoid having n turns per unit length and carrying current / when iron core is kept in it is `(mu_o` = permeability of vacuum, `chi` = magnetic susceptibility)

Options

A. `mu_0nl(1-Chi)`
B. `mu_0nlchi`
C. `mu_0nl^2(1+chi)`
D. `mu_0nl(1+chi)`

Answer

D

Explanation

According to question, change in magnetic field due to insertion of iron core is given by
`B^' =mu B`
= `mu_0(1+chi)B` [`because mu = mu_0(1+chi)]`
where, B=magnetic field in air
`mu_0` = permeability of vacuum
`chi` = magnetic susceptibility
As we know magnetic field inside the solenoid is given by `B = mu_0nl`
So, `B^' = mu_0 (1+chi)nl`