Force on a current-carrying wire calculator

Worked example

Find F, the force. Given: magnetic flux density B = 0.400 T; current I = 3.00 A; length of wire in the field l = 0.150 m; angle between the wire and the field θ = 90.0°.

1. Write the equation
   F = B I l sin(θ)
2. Substitute the values
   F = 0.4 × 3 × 0.15 × sin(90°)
3. Calculate
   F = 0.18 N
4. Give the answer to 3 significant figures
   F = 0.180 N

Symbols and units

Force on a current-carrying wire: rearranged

• To find force: F = B I l sin(θ)
• To find magnetic flux density: B = F / (I l sin(θ))
• To find current: I = F / (B l sin(θ))
• To find length of wire in the field: l = F / (B I sin(θ))
• To find angle between the wire and the field: θ = sin⁻¹(F / (B I l))

Exam tip

The force is greatest when the wire is at 90° to the field and zero when it is parallel. Use Fleming’s left-hand rule for direction.

Common questions

What is the formula for force on a current-carrying wire?

The equation is F = B I l sin(θ), where F is the force (N); B is the magnetic flux density (T); I is the current (A); l is the length of wire in the field (m); θ is the angle between the wire and the field (°).

What units should I use for force on a current-carrying wire?

In SI units: force in N, magnetic flux density in T, current in A, length of wire in the field in m, angle between the wire and the field in °. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange F = B I l sin(θ)?

Rearranging gives these forms: to find force: F = B I l sin(θ). to find magnetic flux density: B = F / (I l sin(θ)). to find current: I = F / (B l sin(θ)). to find length of wire in the field: l = F / (B I sin(θ)). to find angle between the wire and the field: θ = sin⁻¹(F / (B I l)).