Question

The space inside a toroid is filled with tungusten shoes susceptibility is $6.8\times 10^{-5}$. The percentage increase in the magnetic field will be

• A. $0.0068\%$
• B. $0.068\%$
• C. $0.68\%$
• D. None of these

Answer 1

Answer: (A)

When space inside the toroid is filled with air,
$B_0={\mu }_{0}H$
When filled with tungsten,
$B=\mu H={\mu }_0{\mu }_{r}H={\mu }_0\left(1+{\chi }_m\right)H$
Percentage increase in magnetic field/induction
$=\frac{\left(B-B_0\right)\times 100}{B_0}=\frac{{\mu }_0{\chi }_{m}H\times 100}{{\mu }_{0}H}$
$={\chi }_m\times 100$
$=6.8\times 10^{-5}\times 100=0.0068\%$