The force on a current-carrying conductor in a magnetic field
Pass a current through a conductor in a magnetic field — a force F=BIl·sinα acts on it, pushing it perpendicular to both the current and the field. Change the current, the magnetic field, and the length; the direction is given by the left-hand rule. This is the principle of the electric motor.
I'll give you a target force — set the current, field, length, and angle to reach it. F = B·I·l·sin α.
What just happened?
A current flowing through a conductor placed in a magnetic field was pushed by a force perpendicular to both the direction of the current and the field lines. The larger the current, field, and conductor length, the larger the force.
The force on a current-carrying conductor:
— B is the magnetic flux density (T), I — the current (A), l — the length of the conductor in the field (m), α — the angle between the direction of the current and the field lines. The force is largest when (current perpendicular to the field).
Which direction? The left-hand rule:
Hold your left hand so that the field lines enter the palm, and the straightened fingers point in the direction of the current — then the extended thumb shows the direction of the force . The force is always perpendicular to both the current and the field.
What does this mean in practice?
This is the operating principle of every electric motor: the current in a coil placed in a magnetic field is pushed, which sets the rotor in motion. The same force drives loudspeakers and the needles of analogue meters.
Why you need this for the exam:
F = BIl·sin α plus the left-hand rule solve most problems about a conductor in a magnetic field. Trick: check the angle α — if the current is parallel to the field (α = 0°), the force vanishes, because sin 0° = 0.
Remember: a current-carrying conductor in a magnetic field is pushed by a force F = BIl·sin α, perpendicular to the current and the field — the direction is given by the left-hand rule.
Theory & formulas
The force on a current-carrying conductor
A force acts on a current-carrying conductor placed in a magnetic field: It is largest when the conductor is perpendicular to the field (), and vanishes when it is parallel.
Direction of the force
It is found with the left-hand rule: the field lines enter the palm, the straightened fingers point in the direction of the current, and the extended thumb — the direction of the force.
Origin and applications
This force is the resultant of the Lorentz forces acting on the moving charges in the conductor. It is the operating principle of electric motors, loudspeakers, and moving-needle meters.
Symbols: — the force on the conductor, — the magnetic flux density, — the current, — the length of the conductor in the field, — the angle between the conductor and the field lines.
Frequently asked questions
›Where does the force on the conductor come from?
A magnetic field acts on moving charges (the current); their Lorentz forces add up to the force F=BIl·sinα on the conductor.
›How do you find the direction of the force?
With the left-hand rule: the field lines enter the palm, the fingers point to the current, and the extended thumb — the force.
›Where is this force used?
In electric motors, loudspeakers, and moving-needle meters.
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