The big idea: A wire carrying a current placed across a magnetic field feels a force — a sideways push. This is called the motor effect (it is how electric motors spin).
The push is strongest when the current flows at right angles to the field, and there is no push when the current runs along the field.
[Diagram: phys-free-body] - Available in full study mode
Spot it: Three things meet at the wire and they are all at right angles to each other: the field B, the current I, and the force F.
Reverse the current or reverse the field and the force flips the other way.
The size of the force on the wire depends on the field strength B, the current I, the length of wire in the field L, and the angle between the current and the field:
- force on the wire (N)
- magnetic field strength / flux density (T, tesla)
- current in the wire (A)
- length of wire in the field (m)
- angle between the current and the magnetic field
The most common case: Most questions set the wire at right angles to the field, so θ = 90° and sin θ = 1.
The equation then becomes the simpler F = BIL — that is the form you usually use.
[Diagram: phys-formula-triangle] - Available in full study mode
Worked example — force on a wire
A straight wire of length 0.25 m carries a current of 4.0 A at right angles to a magnetic field of strength 0.30 T. Find the force on the wire.
Solution
- Start with the given formula:
- The wire is at right angles to the field, so θ = 90° and sin θ = 1:
- Put in the numbers (B = 0.30, I = 4.0, L = 0.25):
- Work it out — keep the unit:
Final answer
F = 0.30 N.
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How this is tested: The motor effect shows up two ways in exams.
- Size (Paper 1A / 2): use F = BIL — often rearranged to find B from how the force changes when the current changes. - Direction (Paper 1A): use Fleming's left-hand rule to give the direction of the force on a wire, rod or coil in a field.
Classic trap: if the current runs parallel to the field (θ = 0°, sin 0° = 0) the force is zero — not maximum.
Fleming's left-hand rule: Hold the left hand with thumb and first two fingers at right angles:
- First finger → Field (B), from north to south. - SeCond finger → Current (I). - ThuMb → Motion / force (F).
Reverse the current or the field, and the force reverses.
IB-style question — (a) direction of the force
A horizontal rod lies across two rails and carries a current flowing from left to right. A magnetic field points straight out of the page toward you. Use the left-hand rule to state the direction of the force on the rod.
Solution
- First finger = field: point it out of the page (toward you).
- Second finger = current: point it to the right (the way the current flows).
- Thumb then points up the page — that is the force.
Final answer
The force on the rod is directed up the page (toward the top of the diagram).
IB-style question — (b) find the field strength
A 0.20 m length of the same rod sits in the field and carries 5.0 A. The force on it is measured to be 0.60 N, with the current at right angles to the field. Find the magnetic field strength B.
Solution
- Start with the given formula (θ = 90°, so sin θ = 1):
- Rearrange to make B the subject:
- Put in the numbers (F = 0.60, I = 5.0, L = 0.20):
- Work it out — keep the unit:
Final answer
B = 0.60 T.