# Two long straight parallel conductors carry steady current I1, and I2 separated by a distance 'd' if the currents are flowing

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Two long straight parallel conductors carry steady current I1, and I2 separated by a distance 'd' if the currents are flowing 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.

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Fab = Force experienced by wire 'a' of length 'l' due to magnetic field of wire 'b'

Fba = Force experienced by wire 'a' of length 'l' due to magnetic field of wire 'b'

Ba = Magnetic field due to wire 'a'

Bb = Magnetic field due to wire 'b'

The direction of force experienced by the wire 'a' is toward the wire 'b'. (As shown in the diagram).

Similarly the direction of force experienced by the wire 'b' is toward the wire 'a'. Thus, the force is attractive.

If two long wires are placed in vacuum at a separation of 1 m, one Ampere would be defined as the current in each wire that would produce a force of 2 x 10-7 Nm-1 per unit length of wire.