A 250-turn solenoid carries a current of 9.0 A. The radius of the solenoid is 0.075 m; and its length is 0.14 m. Determine the magnetic flux through the circular cross-sectional area at the center of the solenoid. A)1.8 × 10^-⁵ Wb B)9.9 × 10^-⁵ Wb C)3.6 × 10^-⁴ Wb D)7.0 × 10^-⁴ Wb E)2.2 × 10^-³ Wb

Question

Quizplus · Accepted Answer

The magnetic flux through the circular cross-sectional area at the center of the solenoid is given by:
Φ = μ₀n²πr²I
where μ₀ is the permeability of free space (4π × 10^-7 T·m/A), n is the number of turns per unit length (n = N/L = 250/0.14 = 1785.7 turns/m), r is the radius of the solenoid, and I is the current.
Substituting the values, we get:
Φ = (4π × 10^-7 T·m/A)(1785.7 turns/m)²π(0.075 m)²(9.0 A)
Φ ≈ 3.6 × 10^-4 Wb
Therefore, the best choice is (C).

A 250-Turn Solenoid Carries a Current of 9