Final answer:
To produce a magnetic field of 3.0 × 10⁻³ T with a current of 3.7 A, approximately 0.11 turns per centimeter must be wound on the solenoid.
Step-by-step explanation:
To find the number of turns per centimeter required to produce a magnetic field of 3.0 × 10⁻³ T within the solenoid, we can use the formula: B = μ₀nI. where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length (in this case, per centimeter), and I is the current. Rewriting the formula to solve for n: n = B / (μ₀I). Substituting the given values: n = (3.0 × 10⁻³ T) / (4π × 10⁻⁷ T·m/A) / (3.7 A). Simplifying the expression gives:n ≈ 0.11 turns/cm.