Force on a current in a magnetic field: F = BIl
Force = magnetic flux density × current × length. In symbols, F = B I l. F is the force in newtons (N), B is the magnetic flux density in tesla (T), I is the current in amperes (A) and l is the length of wire inside the field in metres (m). Every board prints this Higher tier equation on the sheet in the exam.
Equation
F = B I l
| Symbol | Quantity | Unit |
|---|---|---|
F | force | N |
B | magnetic flux density | T |
I | current | A |
l | conductor length | m |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet · Higher tier only | F = B I l |
| AQA Combined Science (8464) | Given on the sheet · Higher tier only | F = B I l |
| Edexcel Physics (1PH0) | Given on the sheet · Higher tier only | F = B I l |
| Edexcel Combined Science (1SC0) | Given on the sheet · Higher tier only | F = B I l |
| OCR Gateway Physics A (J249) | Given on the sheet · Higher tier only | F = B I l |
| OCR Twenty First Century Physics B (J259) | Given on the sheet · Higher tier only | F = B I l |
Calculator: F = B I l
The motor effect
A wire that carries a current makes its own magnetic field. Put that wire between the poles of a magnet and the two fields push on each other. The wire feels a force. Physicists call this the motor effect.
Electric motors use it to spin a coil. A loudspeaker uses it too: a changing current makes a coil push back and forth on a paper cone, and the cone moves the air to make sound.
Magnetic flux density, B, tells you how strong the field is. Its unit is the tesla. A fridge magnet is a small fraction of a tesla, so GCSE questions often give values like 0.2 T or 0.05 T.
What the boards say
All six specifications print it the same way, F = B I l, and all six mark it as Higher tier. That covers AQA 8463 and 8464, Edexcel 1PH0 and 1SC0, and OCR J249 and J259. So a Foundation paper will not ask you to use it.
It sits on each board's given list, the ones you select and apply. Every physics exam from 2025 comes with a sheet that prints this and all the others. The physics equation sheet page sets out every board's list, and the OCR Gateway page shows where it falls in J249.
Transformers rely on a related effect, where a changing field makes a current. The transformer turns equation is also Higher tier on every board that lists it.
Direction and angle
The equation only works when the wire crosses the field at right angles. If the wire runs parallel to the field lines, there is no force at all.
The size comes from F = B I l. The direction comes from Fleming's left-hand rule. Point your first finger along the field, your second finger along the current, and your thumb shows the push. Reverse the current or flip the magnet and the force reverses.
The current in the wire obeys the circuit equations too. If a question gives you the potential difference and resistance instead, find I first with V = IR.
Worked examples
F
- Change the length to metres: 5 cm = 0.05 m
- F = B I l
- F = 0.2 × 3 × 0.05
- F = 0.03 N
0.03 N
I
- I = F ÷ (B l)
- I = 0.12 ÷ (0.4 × 0.5)
- I = 0.12 ÷ 0.2
- I = 0.6 A
0.6 A
B
- Change the units: 250 mA = 0.25 A and 20 cm = 0.2 m
- B = F ÷ (I l)
- B = 0.015 ÷ (0.25 × 0.2)
- B = 0.015 ÷ 0.05
- B = 0.3 T
0.3 T
Common mistakes
- Using the whole length of the wire. Only the part that sits inside the magnetic field counts as l.
- Leaving the current in milliamps. 250 mA is 0.25 A, and entering 250 makes the flux density 1000 times too small.
- Mixing up the hands. The motor effect uses the left hand; if you use the right, your force points the wrong way.
- Confusing l for length with I for current. In handwriting they look alike, so write a curly ℓ or say the word.
Make B, I or l the subject of F = BIl in the Equation Rearranger.
Questions people ask
What is a tesla?
It is the unit of magnetic flux density. A wire 1 m long carrying 1 A at right angles to a 1 T field feels a force of 1 N.
Why does a motor coil keep turning?
The current flows one way along one side of the coil and the other way along the opposite side. So one side is pushed up and the other down, and the coil turns. A split ring swaps the current every half turn to keep it going.