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

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

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

Answer: (C)

Magnetic flux through a loop in a uniform field depends on how much of the loop’s area is effectively “open” to the field lines. This is captured by Φ = B A cos θ, where θ is the angle between the magnetic field and the loop’s normal (the direction perpendicular to the loop’s plane). The cos function peaks at 1 when θ is 0°, so the largest flux occurs when the loop is oriented with its plane perpendicular to the field (the normal points along the field). In that setup, the field passes straight through the loop, giving the maximum positive flux equal to B A. If the loop lies parallel to the field, the flux drops to zero, and at other angles you get intermediate flux values. If the field is anti-parallel to the normal, the flux is negative but its magnitude can reach the maximum as well; the key for maximum positive flux is having the loop perpendicular to the field.

Magnetic flux through a loop in a uniform field depends on how much of the loop’s area is effectively “open” to the field lines. This is captured by Φ = B A cos θ, where θ is the angle between the magnetic field and the loop’s normal (the direction perpendicular to the loop’s plane). The cos function peaks at 1 when θ is 0°, so the largest flux occurs when the loop is oriented with its plane perpendicular to the field (the normal points along the field). In that setup, the field passes straight through the loop, giving the maximum positive flux equal to B A. If the loop lies parallel to the field, the flux drops to zero, and at other angles you get intermediate flux values. If the field is anti-parallel to the normal, the flux is negative but its magnitude can reach the maximum as well; the key for maximum positive flux is having the loop perpendicular to the field.