Calculate Force on Two Parallel Conductors

[Ry122]

Can someone tell me if I am on the right track with this.

Problem: Two parallel conductors are 15cm apart and carry current of 8 amp and 12 amp. Calculate the size and direction of the force that the conductors exert on each one meter length of each other.

8 amp (out of page) o -------- 15cm --------- x (into page) 12 amp

My attempt:
Left conductor
B=K x (i/d)
B=2x10^-7 x (8/.15)
B=1.06666 x 10^-5
Right conductor
B=K x (i/d)
B=2x10^-7 x (12/.15)
B=1.6 x 10^-5

Since the currents are moving in opposite directions minus the smaller teslas from the larger.
1.6x10^-5 - 1.06666 x 10^-5 = 5.3334 x 10^-6

Only the 8amp conductor will experience a force.

F=BiL
F=5.3334 x 10^-6 x 8 x 1
= 4.26672 x 10^-5 N

 

[Doc Al]

First find the magnetic field of one current at the location of the other. Then figure out the force per unit length on the current-carrying wire due to that magnetic field of the other wire. You only need to figure it out once, since the force on each will be equal and opposite.