If the current in a circular loop is doubled while the radius remains fixed, the magnetic field at the center will

If the current in a circular loop is doubled while the radius remains fixed, the magnetic field at the center will

• A. Double
• B. Quadruple
• C. Halve
• D. Remain the same

Answer: (A)

The magnetic field at the center scales directly with the current when the loop’s size is fixed. For a single loop of radius R, B at the center is given by B = μ0 I /(2R). With the radius unchanged, doubling the current doubles the field magnitude. The geometry stays the same, so the only change is the current, which linearly increases the field. The direction is unchanged by the current doubling, by the right-hand rule. So the center field becomes twice as large.

The magnetic field at the center scales directly with the current when the loop’s size is fixed. For a single loop of radius R, B at the center is given by B = μ0 I /(2R). With the radius unchanged, doubling the current doubles the field magnitude. The geometry stays the same, so the only change is the current, which linearly increases the field. The direction is unchanged by the current doubling, by the right-hand rule. So the center field becomes twice as large.