The solenoid, the force on a wire and parallel wires

Rewrite F = BIℓ sin θ as B = F ÷ (Iℓ sin θ). One tesla is the flux density in which every metre of wire that carries 1 A at right angles to the field feels a force of 1 N: 1 T = 1 N/(A·m). The same formula gives an angle, sin θ = F ÷ (BIℓ). Two long parallel wires each lie in the field of the other. Wire 2 makes the field B₂ = μ0I₂ ÷ (2πd) at wire 1, and the force on a length ℓ of wire 1 is F = B₂I₁ℓ. So the force per metre is F ÷ ℓ = μ0I₁I₂ ÷ (2πd) = 2 × 10⁻⁷ × I₁I₂ ÷ d. By Fleming’s rule, wires with currents in the same direction attract each other, and wires with currents in opposite directions repel each other. The two forces are equal and opposite, as Newton’s third law says: each wire pushes or pulls the other with the same force.