The solenoid, the force on a wire and parallel wires

A wire that carries a current in a magnetic field feels a force, because the field acts on the moving charges in the wire. The force is perpendicular to the wire and also perpendicular to the field. Its size is F = BIℓ sin θ, where ℓ is the length of wire in the field and θ is the angle that the wire makes with the direction of the field. It is largest at θ = 90°, where F = BIℓ, and zero when the wire lies along the field (θ = 0°). More current, a longer wire or a stronger field gives a bigger force. The direction comes from Fleming’s left-hand rule: hold the forefinger, middle finger and thumb of the left hand at right angles; the forefinger points along the field B, the middle finger along the conventional current I, and the thumb shows the force F. Reverse the current or the field and the force reverses; reverse both and it stays the same. In this course directions are given as east, north and up.