A uniform magnetic field passes through two areas, A₁ and A₂. The angles between the magnetic field and the normals of areas A₁and A₂are 30.0° and 60.0°, respectively. If the magnetic flux through the two areas is the same, what is the ratio A₁/A₂? A)0.354 B)0.866 C)1.00 D)1.23 E)1.73

Question

Quizplus · Accepted Answer

The magnetic flux through an area is given by the equation Φ = BAcosθ, where B is the magnetic field strength, A is the area, and θ is the angle between the magnetic field and the normal to the area. If the magnetic flux through two areas is the same, then BAcosθ1 = BAcosθ2. Since the magnetic field strength and the angle between the magnetic field and the normal to the area are the same for both areas, then A1cosθ1 = A2cosθ2. Therefore, A1/A2 = cosθ2/cosθ1 = cos60.0°/cos30.0° = 0.354.

A Uniform Magnetic Field Passes Through Two Areas, A1 and A2

A Uniform Magnetic Field Passes Through Two Areas, A₁ and A₂