Question

A single-turn square loop of side L is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has 1200 turns per meter and a diameter of 5.60 cm , and carries a current of 2.15 A .

Part A: Find the magnetic flux through the loop when L = 2.25 cm.

Φ1 = ____________ Wb

Part B: Find the magnetic flux through the loop when L = 5.60 cm.

Φ2 = ____________ Wb

Part C: Find the magnetic flux through the loop when L = 11.0 cm.

Φ3 = ____________ Wb

Answer 1

Magnetic field due to solenoid, B_s = μ_oni

Magnetic flux through the square loop, Φ = B_s.A = (μ_oni)A

where A is the area of the square loop or the solenoid depending on which one is smaller.

A) Φ = (4π * 10^-7) * 1200 * 2.15 * (2.25 * 10^-2)² = 1.64 * 10^-6 Wb

B) Φ = (4π * 10^-7) * 1200 * 2.15 * [π * (5.60 * 10^-2)² / 4] = 7.99 * 10^-6 Wb

C) Φ = (4π * 10^-7) * 1200 * 2.15 * [π * (5.60 * 10^-2)² / 4] = 7.99 * 10^-6 Wb

Since the magnetic field outside the solenoid is neglgible, the magnetic flux in B and C are equal.