Two long straight parallel conductors carry steady current I1 and I2 separated by a distance d. If the currents are flowing in the same direction,show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.                 (3)

 

                                                12

As shown in figure,the direction of force on conductor b is attractive  12   [Alternatively: 

B at a point on wire 2, is long -k^

F,on wire 2 , due to the B,is a long -l^,i.e.

towards wire1. Hence the force is attractive.

Magnetic field,due to current in conductor a,

                                  B1=u0I12πd                                           12

The magnitude of force on a length L of conductor b,

                         F2=I2LB1                                                       12

                         F2=u0I1I2L2πd

One amphere is that steady current which, when maintained in each of the two very long, straight, parallel conductors, placed one meter apart in vacuum,would produce on each of these conductors a force equal to 2×10-7 newton per meter of their length.                                                                           (1)

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