Final answer:
To produce a magnetic field of 4.4×10⁻⁵ T at its center, a circular coil of radius 15 cm carrying a current of 1 A must have approximately 21 turns.
Step-by-step explanation:
To determine how many turns must be wound on a flat, circular coil of radius 15 cm to produce a magnetic field of magnitude at least 4.4×10⁻⁵ T at the center of the coil when the current through it is 1 A, we will use the formula for the magnetic field (B) at the center of a circular coil carrying current (I):
B = µ₀ * (N * I) / (2 * R),
where µ₀ is the permeability of free space (1.25663706 × 10⁻⁶ T*m/A), N is the number of turns, and R is the radius of the coil.
After rearranging the formula to solve for N:
N = (B * 2 * R) / (µ₀ * I),
and plugging in the given values:
N = (4.4×10⁻⁵ T * 2 * 0.15 m) / (1.25663706 × 10⁻⁶ T*m/A * 1 A),
We get the number of turns N required:
N ≈ 21 turns. Therefore, the coil must be wound with approximately 21 turns to achieve the desired magnetic field strength.