Which orientation yields zero magnetic flux through a loop in a uniform magnetic field?

Which orientation yields zero magnetic flux through a loop in a uniform magnetic field?

• A. Perpendicular to the field
• B. 45 degrees to the field
• C. Anti-parallel to the field
• D. Parallel to the field

Answer: (D)

Magnetic flux through a loop depends on how the loop’s area vector aligns with the magnetic field. It’s given by Phi = B A cos theta, where theta is the angle between the magnetic field and the loop’s normal. When the loop’s plane is parallel to the field, the normal is perpendicular to the field, so theta = 90°, cos 90° = 0, and the flux is zero. In this orientation the field lines pass across the plane rather than through its area. In other orientations, the flux is nonzero: perpendicular to the field gives maximum flux, and intermediate angles give intermediate flux values. If the loop is anti-parallel, the flux is negative but still nonzero. So the orientation that yields zero flux is the loop being parallel to the magnetic field.

Magnetic flux through a loop depends on how the loop’s area vector aligns with the magnetic field. It’s given by Phi = B A cos theta, where theta is the angle between the magnetic field and the loop’s normal. When the loop’s plane is parallel to the field, the normal is perpendicular to the field, so theta = 90°, cos 90° = 0, and the flux is zero. In this orientation the field lines pass across the plane rather than through its area. In other orientations, the flux is nonzero: perpendicular to the field gives maximum flux, and intermediate angles give intermediate flux values. If the loop is anti-parallel, the flux is negative but still nonzero. So the orientation that yields zero flux is the loop being parallel to the magnetic field.