Two long straight parallel conductors carry steady currents I1 and I2 separated by a distance d. If the currents flow in the same direction, show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.
Solution
Conductor 1 produces at conductor 2 a field B1=2πdμ0I1, perpendicular to conductor 2. The force on a length ℓ of conductor 2 is
F=B1I2ℓ=2πdμ0I1I2ℓ⇒ℓF=2πdμ0I1I2.
By Fleming's left-hand rule the force is attractive when the currents are parallel. \textbf{Definition:} one ampere is the current which, in each of two infinite parallel wires 1m apart in vacuum, produces a force of 2×10−7N per metre.
