Library / Electrical / ELE-14
Electrical
Force on a current
Force on a straight conductor carrying current at right angles to a magnetic field.
- Ref
- ELE-14
- Rev
- v1
- Field
- Electrical
- Result
- F [N]
F in newtons, B in tesla, I in amperes, L in metres of conductor inside the field. The conductor must be at right angles to the field. Otherwise F = BIL sin θ.
A wire carrying current in a magnetic field is pushed sideways. The force grows with the field strength, the current and the length of wire in the field. It is the principle behind electric motors and loudspeakers.
Calculator
- Force per metre F/L5 N/m
- Force if the wire is at 45° to the field0.7071 N
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Force is proportional to each of B, I and L, so doubling any one doubles F. In practice B is the hardest to increase.
- Force per metre is just BI. A 10 A current in a 0.5 T field gives 5 N for each metre of wire in the field.
- The force acts at right angles to both the field and the current (Fleming’s left-hand rule), and is zero if the wire lies along the field.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| I Current | 0.1 to 100 A | 0.01 | 10 | 9.99 | +10% | +10 % |
| L Length in the field | 0.01 to 2 m | 0.05 | 10 | 9.95 | +10% | +10 % |
| B Magnetic flux density | 0.01 to 2 T | 0.02 | 4 | 3.98 | +10% | +10 % |
Sweep of Current
| Current (A) | Force (N) |
|---|---|
| 0.1 | 0.01 |
| 0.2371 | 0.02371 |
| 0.5623 | 0.05623 |
| 1.334 | 0.1334 |
| 3.162 | 0.3162 |
| 7.499 | 0.7499 |
| 17.78 | 1.778 |
| 42.17 | 4.217 |
| 100 | 10 |
Sweep one variable
Variables and how each one contributes
Force
What the equation gives you. Everything else feeds it.
Magnetic flux density
Strength of the magnetic field, in tesla. Directly proportional: doubling the field doubles the force.
Current
Current in the conductor. Directly proportional: the force follows the current.
Length in the field
Length of conductor that lies inside the field. Directly proportional, but only the length actually inside the field counts.
Worked example with the values above
- Check the geometry: the current is at right angles to the field, so the full formula applies.
- F = BIL = 0.5 × 10 × 0.2 = 1 N.
Assumptions and limits
- Straight conductor at right angles to a uniform magnetic field.
- Only the length L inside the field is counted.
- The magnetic field produced by the conductor itself is ignored.
Common mistakes
- Forgetting sin θ when the wire is not at right angles to the field.
- Using the total wire length instead of the length inside the field.
- Mixing gauss and tesla. 1 T = 10,000 G.
Statistics and uncertainty
The formula is deterministic for a uniform field, but a real magnet’s field varies across the gap and must be measured, typically to within a few percent. For independent errors, δF/F ≈ √[(δB/B)² + (δI/I)² + (δL/L)²]. An angle error matters little near 90°, because sin θ is flat there.
Where it is used
- Force and torque in motors and actuators.
- Voice-coil actuators and loudspeakers.
- First-order force estimates for linear motors.
Maths you need
- Vectors and perpendicular directions: the force is at right angles to both B and I
- Units: T = N / (A·m)