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

Explanation

The magnetic field at the location of .b. produced by the conductor .a. is `B_(a)=(mu_(0)I_(a))/(2pid)`……..(1)
The magnetic force on a segment L of the conductor .b. due to .a. is `F_(ba)=B_(a)l_(b)L` sin `90^(@)`
Using eq.(1),`F_(ba)=(mu_(0)I_(a)I_(b)L)/(2pid)` .This force `F_(ba)` is towards conductor .a..
Similarly ,we can find the magnetic force `F_(ab)` on segment L of the conductor .a. due to .be.
the force `F_(ab)` is equal in magnitude to `F_(ba)` ,and directed towards .b. .Thus `barF_(ba)=-barF_(ab)`
Definition of ampere:One ampere is that steady current which,when maintained in each of the two very long,straight ,parallel conductors of negligible cross-section and placed on metre apart on vacuum (free space),would produce a force of `2xx10^(-7)` newton per metre of length on each other.
(Note:Any other equivalent correct defination with required key terms shoulds be considered)