Write general expression for force between two point charges.

Explanation

Let we have two infinitely long parallel conductors AB and CD.
`I_(1) and I_(2)` be the current flowing through AB and CD respectively.
r = distance between the conductors
`B_(1) = (mu_(0))/(4pi) (2I_(1))/(r) =` Magnetic field produced due to current `I_(1)` flowing through AB at any point L on the conductor CD.
The direction of magnetic field `B_(1)` is perpendicular to the plane of the paper and is directed into the plane (by right hand screw rule).Thus, the conductor CD (through which current `I_(1)` is flowing ) lies in the magnetic field `vecB_(1)` whic is perpendicular to the length of the conductor. Therefore, conductor CD will experience a sideways force on account of the external field `B_(1)` and the force experienced per unit length of the conductor CD in the magnetic field `B_(1)` is given by
`F_(2) = B_(1)I_(2) xx 1 = B_(1)I_(2)`
Using the value of `B_(1)` in eqn (1) we have
`F_(2) = (mu_(0))/(4pi) (2I_(1)I_(2))/(r)`
Applying Fleming.s left hand rule, we find that force `F_(2)` on conductor CD lies in the plane of the paper perpendicular to conductor CD and is directed towards the conductor AB
Similarly, it can be proved that conductor AB also experiences a force due to current `I_(2)` in CD and is given by `F_(1) = (mu_(0))/(4pi) (2I_(1)I_(2))/(r)`, which lies in the plane of paper and perpendicular to conductor AB and is directed towards the conductor CD.
But `F_(1) and F_(2)` are equal and opposite forces and hence these conductors attract each other. If the two conductors carry the current in opposite direction, then these conductors repel each other.
Definition of ampere :
`F = (mu_(0))/(4pi) (2I_(1)I_(2))/(r)`
IF `I_(1) = I_(2) = I` ampere, r = 1 m and `(mu_(0))/(4pi) = 10^(-7)Nm^(-1)`
One Ampere : One ampere is that steady which when maintained in each of the two infinitely long straight parallel conductors of negligible circular cross section, placed one metre apart in free space, would attract or repel each other with a force of `2 xx 10^(-7)` newton per metre of their lengths.