# Force on a current-carrying wire

A wire carrying current I in a field B feels force F = B I L sin theta.

Physics (university) · Part 08: Circuits and magnetism · Card 12 of 12 · Last updated 2026-10-19

## Analogy

The principle of every electric motor.

## Example

**Wire in field**

F = B I L
= 0.2 x 4 x 0.5
= 0.4 N

## In practice

A 0.5 m wire carrying 4 A across a 0.2 T field feels 0.4 N.

## Practice

### Flashcards

- **What is the force on a current-carrying wire?** F = B I L sin theta.

## Questions people ask

### How does an electric motor use this force?

A coil of wire carrying current sits in a magnetic field. The force on the two sides points in opposite directions, so the coil turns. A commutator flips the current each half turn so the coil keeps rotating in the same direction.

### How is this force related to the force on a single charge?

A wire holds many moving charges. Each feels q v B. Adding them up over the length L gives total force BIL, since current times length equals charge times velocity summed over the wire. So the wire formula is the single-charge formula for many charges.

## Related concepts

- [Magnetic field](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-8)
- [Field of a long straight wire](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-9)
- [Magnetic force on a charge](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-10)
- [Circular motion in a field](https://studyvisually.com/learn/science/physics-university/physics-university-part-8/physics-university-part-8-concept-11)

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