Obtain an expression for the force between two straight parallel conductor carrying current. Hence define ampere.

Explanation

Correct figure with direction of force and currents.
`B=(mu_(0))/(2pi)*(I_(1))/(r)`
`F=BI_(2)lsintheta,theta=90^(@)`
`(F)/(l)=(mu_(0))/(2pi)*(I_(1)I_(2))/(r)`
Definition of ampere
Detailed answer:

Consider two infinitely long parallel conductors carrying currents `I_(1) and I_(2)` in the same direction.
Let .d. be the distance of separation between these two conductors.
The current `I_(1)`, in the conductor (1) produces a magnetic field around it as shown in figure
The magnetic field at any point on the conductor (2) due to current `I_(1)` in conductor (1) is given by
`B_(1)=(mu_O)/(4pi)((2I_(1))/(d))`
The direction of `B_(1)` with reference to conductor (2) is perpendicular to the plane of the conductor and is directed vertically downward (i.e., into the plane)
We know, a current carrying conductor of length .l. placed at right angle to the magnetic field (B) experiences a force. which is given by
`F=Bil`
Therefore, force experienced per unit length of Conductor (2) in the magnetic field `B_(1)` is given by
`F_(2)=B_(1)I_(1)`
`=(mu_O)/(4pi)((2I_(1))/(d))I_(2)`
`=(mu_(O))/(4pi)(2I_(1)I_(2))/(d)`
By applying Fleming.s left hand rule to conductor (2) the direction of `F_(2)` is in the plane of the conductor is directed towards conductor (1)
Similarly `F_(1)=(mu_(O))/(4pi)(2I_(1)I_(2))/(d)`
Ampere is that current which if maintained in two infinitely long parallel conductors of negligible cross-section area separated by 1 metre in vacuum causes a force of `2xx10^(-7)N` on each metre of the other wire.