Multiple Choice
A square conducting loop with sides equal to lies such that the plane of the loop is perpendicular to a magnetic field. What is the flux through the loop?
30. Induction and Inductance
Magnetic Flux
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A ring of radius 0.5m lies in the xy-plane. If a magnetic field of magnitude 2 T points at an angle of 22° above the x-axis, what is the magnetic flux through the ring?
A
0.59 Wb
B
0.69 Wb
C
1.46 Wb
D
1.57 Wb
Verified step by step guidance1
Understand that magnetic flux (Φ) through a surface is given by the formula Φ = B * A * cos(θ), where B is the magnetic field strength, A is the area of the surface, and θ is the angle between the magnetic field and the normal to the surface.
Calculate the area (A) of the ring using the formula for the area of a circle: A = π * r², where r is the radius of the ring. Here, r = 0.5 m.
Identify the angle (θ) between the magnetic field and the normal to the surface. Since the ring lies in the xy-plane, the normal to the surface is along the z-axis. The magnetic field is at an angle of 22° above the x-axis, so the angle with the z-axis is 90° - 22°.
Substitute the values into the magnetic flux formula: B = 2 T, A = π * (0.5 m)², and θ = 68° (since θ = 90° - 22°).
Calculate the magnetic flux using the formula Φ = B * A * cos(θ) with the values obtained in the previous steps.
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