Ampère force: a current-carrying conductor in a magnetic field
A copper rod hangs on two thin wires between the poles of an electromagnet. Close the circuit and the magnetic field pushes the current-carrying conductor so that it swings out like a swing. Change the current, the magnetic induction, the length of the conductor and its angle to the field lines, flip the magnet and check the direction of the force with the left-hand rule.
The arrows F, mg and T share one scale: in equilibrium they form a closed triangle. The glowing dots run around the circuit in the direction of the current.
The field between the poles is taken as uniform over the whole swing region. The current is fed through the suspension wires; the forces on the vertical wires are equal and opposite and cancel out. The wires are 25 cm long and the oscillations gradually die out.
The Ampère force is perpendicular both to the current and to the field lines, and its magnitude is F = IBL·sin α: it is largest when the conductor is perpendicular to the B lines and vanishes when it is parallel to them. The direction is found with the left-hand rule: the B lines enter the palm, the four fingers point along the current, the thumb shows the force. Reversing the current or the magnet poles reverses the force, while reversing both leaves it unchanged.
KEY FORMULAS
A magnetic field acts on a current-carrying conductor with a force called the Ampère force. Its magnitude is F = I·B·L·sin α, where I is the current, B is the magnetic induction, L is the length of the conductor in the field and α is the angle between the current and the magnetic field lines. The force is largest when the conductor is perpendicular to the field lines (sin 90° = 1) and zero when it is parallel to them. The force is perpendicular both to the conductor and to the vector B.
Its direction is found with the left-hand rule: hold your left hand so that the magnetic field lines enter the palm and the four outstretched fingers point along the current — then the thumb, bent at 90°, shows the direction of the Ampère force. In the simulator a translucent left hand stands next to the rod and turns together with the field and the current. Press “Reverse current” or “Flip magnet” — the force turns around and the rod swings the other way. If you change both at once, the direction of the force stays the same.
This is a classic school experiment. A rod of mass m hangs on two light wires that also carry the current to it. It is acted on by gravity mg, the tension of the wires T and the horizontal Ampère force F. The rod swings and comes to rest in the equilibrium position where tan φ = F/(mg) = I·B·L/(m·g). Turn on the forces display — the arrows mg, T and F form a closed triangle. The measurements panel shows F, the deflection angle, its tangent and the tension; the F(I) graph is a straight line, and the φ(t) graph shows damped oscillations about equilibrium.
Why does this force appear at all? A current is the ordered motion of charged particles, and each of them experiences the Lorentz force in a magnetic field. Added up, these forces give the Ampère force: F = N·q·v·B = I·B·L. Electric motors, loudspeakers, moving-coil meters and electromagnetic railguns all work on the Ampère force. Turn the magnet so that the field lines run along the conductor — and the rod hangs straight down, because at α = 0 the force vanishes. The “Check yourself” box asks you to predict where the conductor will swing first and then test the answer on the model.
First come simulators and problems from this very chapter, then closely related topics of the section.
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Electricity · Electrostatics