# Derive an expression for the force between two parallel conductors carrying currents. Hence define ampere.

#### Let the distance between the two conductors carrying current I1 and I2 be d.

Magnetic field produced by conductor 1 at a distance d, B1=μo4π2I1d

Force acting the conductor 2 placed in this magnetic field F=B1I2L

Thus we get F=μo4π2I1I2dL

Force er unit length of conductor 1 f=μo4π2I1I2d

Now put d=1m, I1=I2=1A and L=1m

We get F=μ22π=2×10−7 N

Thus we define ampere as the current flowing in each conductor separated by a unit distance so that one conductor applies a force of 2×10−7 N on a unit length of another parallel conductor.