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

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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=2×107 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 2×107 N on a unit length of another parallel conductor.


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