Fields & Forces of Wires
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
A current makes a magnetic field. Around a long straight wire, the field forms circles, with B = μ0I/(2πr). A current-carrying wire in a magnetic field feels a force, F = ILB sin θ, so two wires near each other push or pull on each other.
1. The field around a wire
2. Wires pushing on wires
Each wire sits in the other’s field, so each feels a force. By the right-hand rules:
Same direction currents attract. Opposite currents repel.
The forces on the two wires are equal and opposite (Newton’s third law), even if the currents are different.
For the force on a wire, use the same rule as for a positive charge, with the current direction in place of v.
A wire parallel to the field feels no force (θ = 0).
3. Example, then try it
Find the magnetic field 0.050 m from a long wire carrying 20 A.
B = (2 × 10⁻⁷)(20) ÷ 0.050 = 8.0 × 10⁻⁵ T, about twice Earth’s field.
Two long parallel wires are 0.10 m apart. Wire 1 carries 20 A and wire 2 carries 10 A, in the same direction. Find the force on a 2.0 m length of wire 2. Is it attractive or repulsive? What force does wire 1 feel?
Field of wire 1 at wire 2: B = (2 × 10⁻⁷)(20) ÷ 0.10 = 4.0 × 10⁻⁵ T.
Force on wire 2: F = ILB = (10)(2.0)(4.0 × 10⁻⁵) = 8.0 × 10⁻⁴ N.
Direction: same-direction currents, so the wires attract.
Wire 1: the same 8.0 × 10⁻⁴ N, toward wire 2. Check: (20)(2.0)(2 × 10⁻⁷ × 10 ÷ 0.10) = 8.0 × 10⁻⁴ N ✓.
Answer: 8.0 × 10⁻⁴ N attraction on each wire.
4. Common mistakes
Two long parallel wires carry currents in opposite directions. How do they affect each other?
Opposite currents repel; same-direction currents attract.
Ready to practice?
5 questions on Fields & Forces of Wires, each with a hint and an explanation for every wrong answer.