What is the magnetic field magnitude (B) at the center of a flat, circular wire coil of N turns and radius R carrying a steady current I?
Answer and explanation
Correct answer: B. B = μ0 N I / (2 R)
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- Step 1: According to the Biot-Savart Law, the field due to a small current element at the center of a circular loop is: .
- Step 2: Integrating along the entire circumference () for 1 turn:
- Step 3: For a closely wound coil of turns, the fields from all turns add constructively by superposition:
Answer
B = μ0 N I / (2 R)
Why not the others: 'B = μ0 N I / (2 π R)' confuses the circular loop formula with an infinite straight wire; 'B = μ0 N I R^2 / 2' is dimensionally wrong; 'B = μ0 I / (4 π R)' is the field at the center of a semicircle.
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