Question

The magnetic field at the center of a current-carrying circular loop is B. If the radius of the loop is doubled, keeping the current unchanged, the magnetic field at the center of the loop will become:

A-B
B-2B
C-B/2
D-4B

Answer 1

The magnetic field at the center of a current-carrying loop is inversely proportional to its radius. Doubling the loop's radius halves the magnetic field, so the new magnetic field would be B/2, not 4B.

Step-by-step explanation:

The question pertains to the magnetic field produced at the center of a current-carrying circular loop. According to the formula for the magnetic field strength at the center of a circular loop, B is inversely proportional to the radius R of the loop. Specifically, the magnetic field at the center is given by the formula B = μ_0 I / (2R), where μ_0 is the permeability of free space, and I is the current through the loop.

If the radius R of the loop is doubled, and the current I remains unchanged, the new magnetic field B' at the center will be B/2 due to the doubled denominator in the formula. Because the formula involves only R, and not R^2, there is no squaring involved when adjusting for changes in radius, contradicting the assumption that the field would become 4B. Hence, the correct answer is that the magnetic field becomes B/2, not 4B.