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

Explanation

In the above figure.
X and Y are the two infinitely long straight parallel conductors, `I_1` and `I_2` are the currents in the X and Y respectively and .d. is the perpendicular distance between the conductors.
Magnetic field due to the current `I_1` is
`B_1=(mu_0I_1)/(2pi d) rarr (1)`
According to right hand clasp rule, the direction of `B_1` is perpendicular to the plane of the paper and directed inwards. The conductor Y lies in the magnetic field `B_1` and hence it experiences force.
The force on a segment .I. of the conductor Y is given by
`F_1 = B_1I_2sin theta" "( :. F = BIlsin theta)`
`F_1 = B_1I_2l rarr (2)" "(:. theta = 90^@ "then" sin 90^@ =1)`
(1)in(2) `implies F_1 =(mu_0I_1I_2l)/(2pi d)`
similarly `F_2=(mu_0I_1I_2l)/(2pi d)`
According to fleming.s left hand rule, `F_1` is towards the conductor X and `F_2` is towards the conductor Y i.e, X and Y are attracting each other. When the currents are in the opposite direction, X and Y repels each other. `F_1` and `F_2` are the mutual forces. From Newton.s third law `F_1 = - F_2`
Therefore, the force of attraction or the force of repulsion is given by `F=(mu_0I_1I_2l)/(2pid)`
Definition of Ampere : Ampere is the current which flows through two infinitely long straight parallel conductors separated by a distance 1 metre, placed in free space, causes a force of `2 xx 10^(-7) Nm^(-1)` between them.