A wire is bent into a square and carries current . The same length of wire is bent into a circular loop carrying the same current. The ratio of the magnetic field at the centre of the square to that at the centre of the circle is nearly

Answer and explanation

Correct answer: C. 1.15

  1. Step 1: Let total wire length be . When shaped into a square of four sides, each side has length , and the perpendicular distance from the center to each side is .
  2. Step 2: The magnetic field at the center of the square contributed by all four sides is .
  3. Step 3: When bent into a circle, the circumference is . The magnetic field at the center is .
  4. Step 4: Compute the ratio of magnetic fields: .
Answer
1.15.
Why not the others: 0.81 calculates the inverse ratio of circular field to square field; 0.57 accounts for only half the sides or halves the ratio; 1.62 makes an arithmetic error with the geometric projection factor .

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