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.

 

[ogb p]

Your approach seems to be on the right track. However, there are a few things to consider in order to ensure accuracy in your calculations:

1. The units for magnetic field strength (B) are Tesla (T), not just K. So your final answer for B should be in units of T, not just a numerical value.

2. The direction of the force can be determined by the right-hand rule, where the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field. In this case, the force will be attractive between the two conductors.

3. The force between the two conductors can be calculated using the equation F = μ0 * I1 * I2 * L / (2πd), where μ0 is the permeability of free space (equal to 4π x 10^-7 N/A^2), I1 and I2 are the currents in the two conductors, L is the length of the conductors, and d is the distance between them.

4. So, in this case, the force on each conductor will be F = (4π x 10^-7 N/A^2) * (8 A) * (12 A) * 1 m / (2π * 0.15 m) = 0.0853 N.

Overall, your approach is correct, but make sure to pay attention to units and use the appropriate equations to ensure accuracy in your calculations.