A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T.Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are at an angle of 30°. A)0 T ∙ m² B)3.1 × 10^-3 T ∙ m² C)5.5 × 10^-³ T ∙ m² D)6.3 × 10^-3 T ∙ m²

Question

Quizplus · Accepted Answer

The magnetic flux through a circular loop is given by the formula Φ = BAcosθ, where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field vector and the plane of the loop. In this problem, B = 0.20 T, A = πr^2 = π(0.10 m)^2 = 0.0314 m^2, and θ = 30° = π/6 radians. Thus, the magnetic flux through the loop is Φ = (0.20 T)(0.0314 m^2)cos(π/6) = 0.031 T∙m^2∙cos(30°) = 3.1 × 10^-3 T∙m^2. Therefore, the best choice is B.

A Flat Circular Loop of Radius 0