Put a current in a magnetic field and the wire is pushed sideways. The size of that push defines what we mean by the strength of the field, and its direction follows a simple hand rule.
A current-carrying conductor in a magnetic field feels a force F = BIL sinθ, where θ is the angle between the current and the field. The force is perpendicular to both, given by Fleming's left-hand rule. Rearranging the perpendicular case defines the magnetic flux density: B = F / (IL), measured in tesla (T).
Vary the flux density B, the current I, the length L in the field and the angle θ. The force comes straight out of the page, with a size that follows F = BIL sinθ. Rotate the wire to lie along the field and watch the force fall to zero.
The force law is the route to a definition of field strength.
The angle factor is sinθ, not cosθ, and θ is between the current and the field: the force is a maximum when they are perpendicular and zero when parallel. Use the left hand for the motor effect (force on a current); the right hand is for induction. The flux density B is defined from F = BIL, so its unit, the tesla, is N A⁻¹ m⁻¹.
Four quick checks on the motor effect and flux density. Each correct answer earns XP and lights this skill on your star map.
The force F = BIL sinθ on a conductor is greatest when the angle θ between the current and the field is:
The tesla, the unit of magnetic flux density, is equivalent to:
In Fleming's left-hand rule the first finger, second finger and thumb represent, in that order:
A straight wire of length 0.20 m carries a current of 5.0 A at right angles to a uniform field of flux density 0.40 T. The force on the wire is:
In calculations, check the angle: if the wire is perpendicular to the field, sinθ = 1 and F = BIL; otherwise include sinθ. Keep SI units (B in T, I in A, L in m gives F in N). When asked to find B, state it as the force per unit current per unit length on a wire at right angles to the field.
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