A uniform magnetic field passes through two areas,A₁ and A₂.The angles between the magnetic field and the normals of areas A₁ and A₂ are 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 is the same for both areas, we can divide both sides of the equation by B to get Acosθ1 = Acosθ2. Substituting the given angles, we get Acos30° = Acos60°. Solving for the ratio A1/A2, we get A1/A2 = cos60°/cos30° = 0.866.

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