GATE 2016 EE – Question 24
A soft-iron toroid is concentric with a long straight conductor carrying a direct current $I$. If the relative permeability $\mu_r$ of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is ________.
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Correct answer: 99 to 101
Explanation
The magnetic field strength $H$ from the straight conductor is the same just inside and just outside the toroid surface. The flux density is $B = \mu H$, so the ratio of the density inside the soft iron to that outside in air is $\frac{\mu_0 \mu_r H}{\mu_0 H} = \mu_r = 100$.