Case 1
- Magnetic field strength
- 0.5T
- Current through the wire
- 10A
- Length of wire inside the field
- 0.2m
1.00N
Open with these valuesMagnetic Force on a Wire Calculator
1.00N
Result: 1.00 NA wire carrying 10 A through a 0.5 T field over 0.2 m feels 1 N. That is the BIL rule: field times current times the length of wire inside the field. It assumes the current runs perpendicular to the field, which gives the largest force; at an angle θ the force falls by sin θ.
The numbers at a glance
Held fixed: Magnetic field strength 0.5000 T, Current through the wire 10.000 A.
| Length of wire inside the field (m) | Result (N) |
|---|---|
| 0.0500 | 0.25 |
| 0.1000 | 0.50 |
| 0.1500 | 0.75 |
| 0.2000Your value | 1.00 |
| 0.2500 | 1.25 |
| 0.3000 | 1.50 |
| 0.3500 | 1.75 |
| 0.4000 | 2.00 |
Worked examples
Case 2
- Magnetic field strength
- 2T
- Current through the wire
- 5A
- Length of wire inside the field
- 3m
30.00N
Open with these valuesCase 3
- Magnetic field strength
- 1.5T
- Current through the wire
- 100A
- Length of wire inside the field
- 0.25m
37.50N
Open with these valuesHow it's calculated
F = B × I × L
- StepEnter the flux density B in tesla — an MRI scanner is around 1.5 T.
- StepEnter the current in amperes.
- StepEnter only the length of wire that actually sits inside the field.
- ResultRead the force in newtons; reversing current or field reverses it.
Reference table
| Field, current, length | Setting | Force (N) |
|---|---|---|
| 0.05, 2, 1.5 | Weak field, long wire | 0.15 |
| 0.5, 10, 0.2 | Loudspeaker voice coil | 1 |
| 1, 1, 1 | One tesla, one amp, one metre | 1 |
| 2, 5, 3 | Strong magnet, three-metre bar | 30 |
| 1.5, 100, 0.25 | Motor winding at high current | 37.5 |
Questions
How do I calculate the magnetic force on a wire?
Multiply the field strength by the current and by the length of wire inside the field: F = B × I × L. Use tesla, amperes and metres to get the force in newtons. A wire in a 0.5 T field carrying 10 A over 0.2 m feels 1 N.
What is the BIL formula?
BIL is shorthand for F = B × I × L, the force on a straight current-carrying conductor in a magnetic field. B is the flux density in tesla, I the current in amperes and L the length of wire in the field in metres. It is the basis of how electric motors and loudspeakers turn current into motion.
Does the wire have to be perpendicular to the field?
The simple formula assumes the current runs perpendicular to the field, which gives the maximum force. In general F = B × I × L × sin θ, where θ is the angle between wire and field. A wire lying along the field feels no force at all.
Which units should I use?
Tesla for the field, amperes for the current and metres for the wire length, which gives the force in newtons. One tesla is a strong field: a typical fridge magnet is about 0.01 T, while an MRI scanner reaches around 1.5 T.
Where does this force show up in real life?
It makes electric motors spin and drives the cone of a loudspeaker. Reversing either the current or the field direction reverses the force, which is exactly how a motor keeps turning the same way.
Sources and last check
Information, not professional advice.