Question

Magnetic field inside long solenoid changes from $2\times {10}^{-3}T$ to $1T$ when it is filled with some ferromagnetic material. Susceptibility of this material is

• A. $6.8\times {10}^{-5}$
• B. $-5\times {10}^{-4}$
• C. $849$
• D. $499$

Answer 1

The correct option is D $499$

$B={\mu }_0(H+I)$ & $I=XH\Rightarrow B={\mu }_0(H+XH)$
$B_{air}={\mu }_0(1+X_{air})H$ & $B_{Material}={\mu }_0(1+X_{mat})H$
$X_{air}=0\Rightarrow \frac{B_{air}}{B_{mat}}=\frac{{\mu }_{0}H}{{\mu }_{0}H(1+X_{mat})}$
$\frac{2\times {10}^{-3}}{1}=\frac{1}{1+X_{mat}}\Rightarrow 1+X_{mat}=500$
$X_{mat}=499$