Force Between Parallel Conductors

[miniradman]

Hi there, I really need help with one question and help/hints would be greatly appreciated

1. A wire 3meters long, mass 0.10kg and carrying a current of 70.0 Amps floats without support above a horizontal wire 2.0cm below and parrallel to it. Find the current in the lower wire



2. I'm guessing this could be relevant formulas area? this formula

F/L = µo/2(pi) * I1 I2/d

where:
L= 3.00m
I1(subscript 1) = 70.00A
I2(subscript 2) = ?
d= 2cm or 0.02m



3. This is the exact working out that I have attempted

1/3 = (4(pi)*10^-7)/2(pi) * (70.0 I2/0.02)

= (8.79*10^-5)I2/0.125

*I am confused about the weight

 

[omoplata]

Apply Newton's 2nd law to the floating wire. Then you can find F. Then all you have to do is solve for I2.

 

[miniradman]

Oh thanks mate, that was a lot of help!

(I feel dumb now)

Cheers!

 

[omoplata]

No problem.

I had trouble with those problems once too.

 

[rwisz]

of the wire and how it affects the formula



I would first clarify the question and make sure I understand the scenario correctly. From the given information, it seems that we have two parallel wires, one of length 3m and mass 0.10kg, carrying a current of 70.0 Amps. The other wire is 2.0cm below and also parallel to the first wire, and we need to find the current in the lower wire.

To solve this problem, we can use the formula for the force between parallel conductors, which you have correctly identified. However, we also need to take into account the weight of the wire, as it is floating without support. This weight will create a downward force that needs to be balanced by the magnetic force between the two wires.

To incorporate the weight of the wire into the formula, we can use the formula F = mg, where m is the mass of the wire and g is the acceleration due to gravity. Since the wire is floating, we can assume that it is not accelerating, so we can set F = mg equal to the magnetic force between the wires.

Thus, our final formula becomes F/L = µo/2(pi) * I1 I2/d + mg, where m is the mass of the wire and g is the acceleration due to gravity. We can now plug in the given values and solve for I2.

I hope this helps. Let me know if you have any further questions or need clarification. Best of luck with your problem!