AP® Physics 2: Algebra-Based · Unit 12 · Topic 12.3
Forces Between Parallel Wires
Each current-carrying wire makes a magnetic field that pushes or pulls on the moving charges in the other wire, so parallel wires with current in the same direction attract and opposite directions repel.
A wire carrying current makes a magnetic field that curls around it, field lines forming circles centered on the wire. If you put a second current-carrying wire nearby, it sits inside that field. A current in a magnetic field feels a force, F = I·L·B, so the second wire gets pushed. Work out the direction with the right-hand rule and you find that currents flowing the same way attract, and currents flowing opposite ways repel. Each wire is just reacting to the other's field, not touching it, not sensing any charge on it, only sensing the magnetic field that field creates.
The strength of this force follows directly from combining the formula for the field of a long straight wire, B = mu0·I/(2·π·d), with the force on a current in a field, F = I·L·B. Substitute one into the other and divide by length to get the force per unit length: F/L = mu0·I1·I2/(2·π·d). Plug in mu0 = 4·π x 10−7, and the formula simplifies nicely to F/L = 2 x 10−7·I1·I2/d, with I in amps, d in meters, and F/L in newtons per meter.
This result is actually how the ampere itself used to be defined: two wires one meter apart, each carrying one amp, pull on each other with a force of exactly 2 x 10−7 newtons per meter. It connects directly to the idea that magnetism is charge in motion, the same moving-charge story that explains why a single charged particle curves in a magnetic field, just scaled up to a whole wire of moving charges.
Key terms
- mu0 (permeability of free space)
- A constant, 4·π x 10−7 T·m/A, that sets the strength of magnetic fields made by currents.
- Force per unit length
- The magnetic force divided by the length of wire over which it acts, measured in newtons per meter.
- Right-hand rule
- A way to find the direction of a magnetic field or force by pointing the fingers or thumb of the right hand along current or field directions.
- Electrically neutral
- Having equal amounts of positive and negative charge, so the net charge is zero.
Watch it explained
- How it worksHow does one wire's field grab the current in the neighboring wire and produce a force?
- Worked exampleFind the force per meter between two wires 0.02 m apart carrying 10 A each in the same direction.
- Common mistakeWhy isn't the attraction between parallel currents an electrostatic effect between the wires?
Check yourself
End of topic.