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Two wires A and B are identical, each having length l and carrying the same current I. Wire A is shaped into a circular loop of radius R, while wire B is bent into a square of side a. If the magnetic fields at the centers of the circle and the square are BA and BB respectively, what is the value of BA/BB?

1. π²/16
2. π²/(8√2)
3. π²/8
4. π²/(16√2)

Correct answer: π²/(8√2)

Solution

The magnetic field at the center of a circular loop is given by the formula B = (μ₀I)/(2R), while for a square loop, it can be derived to be B = (μ₀I)/(4a) multiplied by a correction factor due to the geometry. Given that the side length a of the square is related to the radius R of the circle, the ratio BA/BB simplifies to π²/(8√2), making option B the correct answer.

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