If the loop radius R is doubled while keeping current I fixed, how does the magnetic field at the center change?

If the loop radius R is doubled while keeping current I fixed, how does the magnetic field at the center change?

• A. Doubles
• B. Halves
• C. Becomes quarter
• D. Remains the same

Answer: (B)

At the center of a circular loop, the magnetic field from a current I is B = μ0 I / (2R). This shows the field is inversely proportional to the radius for a fixed current. If the radius is doubled, the denominator doubles, so the field becomes half of its original value. The intuition is that spreading the same current over a larger loop weakens the magnetic influence at the center. The magnitude is halved (the direction would still be along the axis given by the right-hand rule, if you care about orientation).

At the center of a circular loop, the magnetic field from a current I is B = μ0 I / (2R). This shows the field is inversely proportional to the radius for a fixed current. If the radius is doubled, the denominator doubles, so the field becomes half of its original value. The intuition is that spreading the same current over a larger loop weakens the magnetic influence at the center. The magnitude is halved (the direction would still be along the axis given by the right-hand rule, if you care about orientation).