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.