GATE EE 2016 Set 1 — Question 24
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Electromagnetic Fields → Magnetostatics → Boundary Conditions (H)
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Question
A soft-iron toroid is concentric with a long straight conductor carrying a direct current . If the relative permeability 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 _______.
Correct answer
99 to 101
Solution
Consider a long straight conductor carrying current . The magnetic field intensity at a distance from the conductor is given by . For two adjacent points, one just inside the toroid and one just outside, the distance is approximately the same. Thus, is the same for both points. The magnetic flux density inside the soft-iron toroid is , and the magnetic flux density just outside the toroid (in air) is . The ratio of the magnetic flux densities is . Given , the ratio is 100.
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