Question

A wire bent into circular loop A carries current I. The same wire is bent into loop B with two turns, same current. Find the ratio of magnetic fields at the centers of A to B.

• A. 45673
• B. 16
• C. 4
• D. 45661

Hint:

Consider the relationship between circumference and radius with the number of turns.

Answer 1

The Correct Option is D

The magnetic field at point A is given by \( B_A = \mu₀I/(2r_A) \). The magnetic field at point B, considering two turns, is \( B_B = \mu₀I/r_B \). Given a constant wire length, \( 2\pi r_A = 4\pi r_B \), which implies \( r_B = r_A/2 \). Consequently, the ratio \( B_A/B_B \) is \( 1/4 \).