**Force between two long parallel current-carrying conductors**

AB and CD are two straight very long parallel conductors placed in air at a distance a. They carry currents I_{1} and I_{2} respectively. (Figure). The magnetic induction due to current I_{1} in AB at a distance a is

**B _{1} = (μ_{0}I_{1}/2πα) … … … (1)**

Fig: Force between two long parallel current carrying conductors

This magnetic field acts perpendicular to the plane of the paper and inwards. The conductor CD with current I_{2} is situated in this magnetic field. Hence, force on a segment of length l of CD due to magnetic field B_{1} is

F = B_{1}I_{2}*l*

substituting equation (1)

**F = (μ _{0}I_{1} I_{2}l / 2πα) … … … (2)**

By Fleming’s Left Hand Rule, F acts towards left. Similarly, the magnetic induction due to current I_{2} flowing in CD at a distance a is

**B _{2} = (μ_{0}I_{2}/2πα) … … … (3)**

This magnetic field acts perpendicular to the plane of the paper and outwards. The conductor AB with current I_{1}, is situated in this field. Hence force on a segment of length l of AB due to magnetic field B_{2} is

F = B_{2}I_{2}*l*

substituting equation (3)

**F = (μ _{0}I_{1} I_{2}l / 2πα) … … … (4)**

By Fleming’s left hand rule, this force acts towards right. These two forces given in equations (2) and (4) attract each other. Hence, two parallel wires carrying currents in the same direction attract each other and if they carry currents in the opposite direction, repel each other.