Calculate force on a current-carrying wire
Use F = BIL sin θ, determine force direction with Fleming's left-hand rule and define magnetic flux density.
Section 20 · Magnetic fields
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 20. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use current, charge, force, velocity, vectors, area and SI units; distinguish conventional current from electron flow.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
When is the force on a current-carrying wire greatest?
What you will learn
- Explain that a current-carrying conductor can experience force in a magnetic field
- Use F = BIL sin θ
- Define magnetic flux density for a wire at right angles to the field
A current in a magnetic field can experience force
A current-carrying wire in an external magnetic field can experience a force because the moving charges in the wire interact with the field. The force is greatest when the current direction is at right angles to the field and zero when the wire is parallel to it.
For wire length L carrying current I in field B at angle θ to the field, F = BIL sin θ. Use the angle between the current direction and the magnetic field, not the angle between the wire and the page unless those are the same.
Flux density describes force per current and length
When the wire is at right angles to the field, sin θ = 1, so B = F/(IL). Magnetic flux density is the force per unit current per unit length on a wire placed perpendicular to the field. Its unit is the tesla: 1 T = 1 N A⁻¹ m⁻¹.
Fleming's left-hand rule gives the force direction for conventional current: first finger field, second finger current, thumb force. If the current direction or field direction reverses, the force reverses.
Pause and explain
A wire is parallel to a magnetic field. What is its force from F = BIL sin θ?
Worked example
A 0.25 m wire carries 3.0 A at right angles to a 0.40 T field. Find the magnetic force.
Show the worked solution
- Use F = BIL sin θ.
- For 90°, sin θ = 1.
- Substitute the values in SI units.
Answer F = 0.40 × 3.0 × 0.25 = 0.30 N.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 0.40 m wire carries 2.0 A at 30° to a 0.50 T field. Calculate the force magnitude.
Give me a hint
Use the angle between the wire's current and B.
Compare my reasoning
- F = BIL sin θ.
- F = 0.50 × 2.0 × 0.40 × sin 30°.
- F = 0.20 N.
F = 0.20 N.
Look for these in your work
- Correct relation selected
- Angle applied
- Force calculated
A perpendicular wire of length 0.15 m carries 4.0 A and experiences force 0.12 N. Find B.
Give me a hint
For θ = 90°, rearrange F = BIL.
Compare my reasoning
- B = F/(IL).
- B = 0.12/(4.0 × 0.15).
- Give teslas.
B = 0.20 T.
Look for these in your work
- Perpendicular condition used
- Equation rearranged
- Tesla unit stated
The field direction is unchanged, but the conventional current in a wire is reversed. What happens to the magnetic force direction?
Give me a hint
Apply Fleming's left-hand rule or the vector dependence on current direction.
Compare my reasoning
- The field direction stays fixed.
- Reversing current reverses the force direction in the left-hand rule.
- The magnitude stays the same if B, I, L and angle magnitude are unchanged.
The force reverses direction; its magnitude is unchanged under the stated conditions.
Look for these in your work
- Fixed field noted
- Force reversal identified
- Magnitude condition checked
Common mistakes
- Using the angle from the page instead of the angle between current and field
- Omitting sin θ
- Using electron flow instead of conventional current in Fleming's left-hand rule
- Defining B without the perpendicular-wire condition
What can you explain now?
When is the force on a current-carrying wire greatest?
Compare with the explanation
When current is perpendicular to the field
sin θ is greatest at 90°.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Which angle belongs in F = BIL sin θ, and how does Fleming's left-hand rule use the directions?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.