Question

The magnetic field (B) inside a long solenoid having 'n', turns per unit length and carrying current 'I' when iron core is kept in it is (${\mu }_0$ = permeability of vacuum, $\chi$ = magnetic susceptibility)

• A. ${\mu }_{0}nI(1-\chi )$
• B. ${\mu }_{0}nI\chi$
• C. ${\mu }_{0}n{I}^2(1+\chi )$
• D. ${\mu }_{0}nI(1+\chi )$

Answer 1

Answer: (D)

${\mu }_{0}nI(1+\chi )$

Magnetic field due to solenoid $=\mu \times n\times I$

where $\mu =$ permeability

$n=$ turn density

$I=$ current

Also $\mu ={\mu }_0(1+\chi )$

where $\chi =$ magnetic susceptibility

$B_{solenoid}={\mu }_{0}nI(1+\chi )$