If the radius R of a single-turn circular loop carrying current I is doubled, the magnetic field at the center becomes what?

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If the radius R of a single-turn circular loop carrying current I is doubled, the magnetic field at the center becomes what?

The magnetic field at the center of a single circular loop depends inversely on the loop’s radius. For a thin loop, B at the center is given by B = μ0 I / (2R). If the radius is doubled, the new field is B' = μ0 I / (2(2R)) = (1/2) × (μ0 I / (2R)) = B/2. So the field becomes half of its original value. This happens because increasing the loop’s size places current elements farther from the center, reducing their contributions to the center field, and the 1/R relationship captures that geometric effect.

The magnetic field at the center of a single circular loop depends inversely on the loop’s radius. For a thin loop, B at the center is given by B = μ0 I / (2R). If the radius is doubled, the new field is B' = μ0 I / (2(2R)) = (1/2) × (μ0 I / (2R)) = B/2. So the field becomes half of its original value. This happens because increasing the loop’s size places current elements farther from the center, reducing their contributions to the center field, and the 1/R relationship captures that geometric effect.

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