AcademyMagnetic Fields and Forces
Academy
Forces on Current-Carrying Conductors
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
A current-carrying conductor feels magnetic force because its moving charges feel magnetic force.
Notation
\(\vec F\)
magnetic force on a wire segment
\(\mathrm{N}\)
\(I\)
conventional current
\(\mathrm{A}\)
\(\vec L\)
length vector in current direction
\(\mathrm{m}\)
\(\vec B\)
magnetic field
\(\mathrm{T}\)
\(\theta\)
angle between current and field
\(\mathrm{rad}\)
Method
Add the magnetic forces on the drifting charges in a wire segment. The result is a force on the conductor.
Wire force law
\[\vec F=I\vec L\times\vec B\]
Magnitude
\[F=ILB\sin\theta\]
Perpendicular case
\[F=ILB\]
The length vector points in the direction of conventional current. The force direction follows the right-hand rule for \(\vec L\times\vec B\).
Rules
Wire force
\[\vec F=I\vec L\times\vec B\]
Wire force magnitude
\[F=ILB\sin\theta\]
Force per length
\[\frac{F}{L}=IB\sin\theta\]
Examples
Question
A
\[0.40\,\mathrm{m}\]
wire carries \[5.0\,\mathrm{A}\]
perpendicular to \[0.20\,\mathrm{T}\]
Find the force.Answer
\[F=ILB=(5.0)(0.40)(0.20)=0.40\,\mathrm{N}\]
Checks
- Use conventional current direction for \(\vec L\).
- The force is zero when current is parallel to the field.
- The force direction is perpendicular to both the current direction and the magnetic field.