A 2.00-m long metal wire is formed into a square and placed in the horizontal xy-plane.A uniform $\vec { B }$ field is oriented at 30° above the horizontal with a magnitude of 0.344 T.What is the magnetic flux through the square due to this field? A)0.0745 T ∙ m² B)0.172 T ∙ m² C)0.0430 T ∙ m² D)0.298 T ∙ m²

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Quizplus · Accepted Answer

The magnetic flux through a surface is given by the product of the magnetic field perpendicular to the surface and the area of the surface. In this case, the wire forms a square, so the area of the surface is given by A = L^2 = (2.00 m)^2 = 4.00 m^2. The component of the magnetic field that is perpendicular to the square can be found using trigonometry. We can see from the diagram that the angle between the magnetic field and the normal to the square is 60°. Therefore, the component of the magnetic field perpendicular to the square is given by: B_perp = B sin 60° = (0.344 T)(0.866) = 0.298 T Therefore, the magnetic flux through the square is given by: Φ = B_perp A = (0.298 T)(4.00 m^2) = 1.19 T·m^2 However, the answer choices are given in units of T·m^2 with a prefix. To convert 1.19 T·m^2 to one of the answer choices, we can simply move the decimal point. 0.119 T·m^2 = 0.0430 T·m²

A 200-M Long Metal Wire Is Formed into a Square and and Placed