A straight wire of length L carrying current I is placed in a uniform magnetic field B perpendicular to the wire. What is the magnitude of the magnetic force on the wire?

A straight wire of length L carrying current I is placed in a uniform magnetic field B perpendicular to the wire. What is the magnitude of the magnetic force on the wire?

• A. F = I L B
• B. F = μ0 I L B
• C. F = I B / L
• D. F = B I / L

Answer: (A)

The key idea is the force on a current-carrying wire in a magnetic field, given by the cross product dF = I dl × B. If the magnetic field is perpendicular to the wire, the angle between dl (along the wire) and B is 90°, so the magnitude is dF = I B dl. For a wire of length L in a uniform field, you sum (integrate) along the whole length: F = ∫ I B dl = I B ∫ dl = I B L. So the force magnitude is I L B, independent of any 1/L factor or μ0. The direction is perpendicular to both the current and the field, found by the right-hand rule. The other forms don’t fit because μ0 isn’t part of the force law once B is given, and expressions like I B / L or μ0 I L B would imply incorrect dependence on length or field constants.

The key idea is the force on a current-carrying wire in a magnetic field, given by the cross product dF = I dl × B. If the magnetic field is perpendicular to the wire, the angle between dl (along the wire) and B is 90°, so the magnitude is dF = I B dl. For a wire of length L in a uniform field, you sum (integrate) along the whole length: F = ∫ I B dl = I B ∫ dl = I B L. So the force magnitude is I L B, independent of any 1/L factor or μ0. The direction is perpendicular to both the current and the field, found by the right-hand rule.

The other forms don’t fit because μ0 isn’t part of the force law once B is given, and expressions like I B / L or μ0 I L B would imply incorrect dependence on length or field constants.