Magnetic Force on Currents
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
A current is many moving charges, so a field pushes on it too: F = IL × B, or ∫I dl × B for a curved wire. Two currents push on each other: same direction attract, opposite directions repel. A current loop feels a torque, τ = μ × B.
1. Forces between currents
2. Shortcuts worth knowing
Curved wire in a uniform field: the force is the same as on a straight wire joining its ends. A closed loop in a uniform field feels zero net force.
In a non-uniform field (like a wire’s), the near and far sides of a loop feel different forces, so the net force isn’t zero.
Torque on a loop is largest when the field lies in the loop’s plane (μ ⟂ B) and zero when μ lines up with B.
The loop rotates toward μ ∥ B, the lowest-energy position, U = −μB. That’s how a motor and a compass needle work.
3. Example, then try it
A straight 0.80 m wire carries 5.0 A perpendicular to a uniform 0.25 T field. Find the force on it. What angle would make the force zero?
F = ILB = (5.0)(0.80)(0.25) = 1.0 N.
The force is zero when the wire runs parallel to B (θ = 0).
A 100-turn rectangular coil, 4.0 cm × 5.0 cm, carries 0.50 A in a uniform 0.30 T field. Find its magnetic moment, the largest torque it can feel, the torque when μ is at 30° to B, and the work to turn it from aligned (μ ∥ B) to opposite.
Moment: μ = NIA = (100)(0.50)(0.040 × 0.050) = 0.10 A·m².
Largest torque (μ ⟂ B): τ = μB = (0.10)(0.30) = 0.030 N·m.
At 30°: τ = μB sin 30° = 0.015 N·m.
Work: ΔU = (+μB) − (−μB) = 2μB = 0.060 J.
Answer: 0.10 A·m²; 0.030 N·m; 0.015 N·m; 0.060 J.
4. Common mistakes
Two long parallel wires carry currents in opposite directions. What do they do?
Reverse one current and the force on it reverses: opposite currents push apart.
Ready to practice?
4 questions on Magnetic Force on Currents, each with a hint and an explanation for every wrong answer.