Force between identical wires in a circuit (1st post)

[dtchannell88]

1. Two Identical wires denoted A & B are part of an electric circuit and therefore carry some currents. The wires are characterized by resistance per unit length,r, and both have length, L, each are spaced by a distance, a. What is the magnitude, F, of the force the wires exert on each other? Is this force an attractive force? For the given resistance, R of the resistor, what should be the length, L, to achieve maximum possible, F,?

Equations i thought might be useful..:
E=I*((r*L/2) + R)



My attempt:

Since..

I =emf/2rL+R

emf=I*((r*L/2) + R)


Then the force is equal to length, by current, by magnetic field. Because the current is going in the same direction in the two wires it will be an attraction force.

When you get Force as a function of L,
F = (µ0 *E^2)/(2*pi*a*r^2*L) where
µ0=permeability
pi = 3.141592...

Im unsure if this is even right, and where I go from here.. all help is appreciated..

 

[dtchannell88]

FIGURE LINK:
https://www.physicsforums.com/attachment.php?attachmentid=22406&d=1260423568"

 

[kerimek]

First of all, great job on attempting to solve this problem using equations! Your initial approach is on the right track, but there are a few things to clarify and consider. Let's break it down step by step:

1. The first thing to note is that the force between two wires is due to their magnetic fields interacting with each other. This is known as the Lorentz force, given by F = I * L * B, where I is the current, L is the length of the wire, and B is the magnetic field.

2. In this case, the wires are carrying current in the same direction, so the force will be attractive. This is because the magnetic fields produced by the wires will add together, creating a stronger force between them.

3. The equation you provided, F = (µ0 *E^2)/(2*pi*a*r^2*L), is actually the equation for the magnetic field produced by a wire. To calculate the force, we need to use the Lorentz force equation mentioned above.

4. The current in the wires can be calculated using Ohm's law: I = V/R, where V is the voltage and R is the resistance. Since the wires are identical, they will have the same resistance and therefore the same current.

5. Now we can substitute the values for current, length, and magnetic field into the Lorentz force equation to get an equation for the force between the wires: F = I^2 * L * B. Here, B can be calculated using the equation B = µ0 * I/(2*pi*r), where µ0 is the permeability of free space.

6. To maximize the force between the wires, we want to maximize the magnetic field. This can be done by maximizing the current and minimizing the distance between the wires.

In summary, the force between two identical wires in a circuit can be calculated using the Lorentz force equation, and the force will be attractive due to the wires carrying current in the same direction. To achieve maximum force, we can increase the current and decrease the distance between the wires. I hope this helps clarify the problem and guide you in the right direction!