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Q.
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
Magnetism and Matter
Solution:
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
$=\frac{\left(B-B_{0}\right) \times 100}{B_{0}}=\frac{\mu_{0} \chi_{m} H \times 100}{\mu_{0} H}$
$=\chi_{m} \times 100$
$=6.8 \times 10^{-5} \times 100=0.0068 \%$