What is the magnetic force on a straight wire of length L carrying current I in a uniform magnetic field B?

What is the magnetic force on a straight wire of length L carrying current I in a uniform magnetic field B?

• A. F = I L × B; magnitude F = I L B sin φ
• B. F = ILB
• C. F = I B × L
• D. F = I L × B; magnitude F = I L B sin φ

Answer: (D)

The force on a current-carrying wire in a magnetic field comes from the cross product between the wire’s length vector and the magnetic field: F = I (L × B). Here L is the vector along the wire in the direction of the current with magnitude equal to the wire’s length, and B is the magnetic field. The magnitude of that force is F = I L B sin φ, where φ is the angle between the wire’s length vector and the magnetic field. The direction of F is perpendicular to both the wire and the field, given by the right-hand rule: point along the current, rotate toward the field, and the force points along L × B. So the best form is the cross-product expression with the magnitude containing sin φ. If the field is perpendicular to the wire, φ = 90°, and the magnitude becomes F = I L B. If the field is parallel to the wire, φ = 0°, giving no force. The other options miss either the vector nature (cross product) or the angle dependence, or in the case of swapping order, would point in the opposite direction.

The force on a current-carrying wire in a magnetic field comes from the cross product between the wire’s length vector and the magnetic field: F = I (L × B). Here L is the vector along the wire in the direction of the current with magnitude equal to the wire’s length, and B is the magnetic field. The magnitude of that force is F = I L B sin φ, where φ is the angle between the wire’s length vector and the magnetic field. The direction of F is perpendicular to both the wire and the field, given by the right-hand rule: point along the current, rotate toward the field, and the force points along L × B.

So the best form is the cross-product expression with the magnitude containing sin φ. If the field is perpendicular to the wire, φ = 90°, and the magnitude becomes F = I L B. If the field is parallel to the wire, φ = 0°, giving no force. The other options miss either the vector nature (cross product) or the angle dependence, or in the case of swapping order, would point in the opposite direction.