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_0nI(I-chi)`
B. `mu_0nLchi`
C. `mu_0nI^(2)(I+chi)`
D. `mu_0nI(I+chi)`

Answer

D

Explanation

The magnetic field inside the solenoid is `B=muH` where ` mu=mu_0mu_R and H=nI` where n is the number of turns per meter of the solenoid. `therefore B=mu_0mu_R and H=nI` The relation between `mu_R and x` is given by `mu_r=X+1 therefore B=mu_0(X+1)nI or B=mu_0nI(1+X)`.