Final answer:
Approximately 480 turns must be wound on the flat, circular coil to produce a magnetic field of magnitude 4.0 × 10⁻⁵ T at the center of the coil when the current through it is 1 A.
Step-by-step explanation:
To calculate the number of turns required to produce a magnetic field of a given magnitude, we can use the formula:
B = (μ₀ * n * I) / (2 * R)
Where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), n is the number of turns, I is the current, and R is the radius of the coil.
In this case, we have the values B = 4.0 × 10⁻⁵ T, I = 1 A, and R = 0.15 m. Plugging these values into the formula, we can solve for n:
n = (B * 2 * R) / (μ₀ * I)
Substituting the given values:
n = (4.0 × 10⁻⁵ T * 2 * 0.15 m) / (4π × 10⁻⁷ T·m/A * 1 A)
Simplifying the equation:
n = 4.8 × 10² turns
Therefore, approximately 480 turns must be wound on the flat, circular coil to produce a magnetic field of magnitude 4.0 × 10⁻⁵ T at the center of the coil when the current through it is 1 A.