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

• dtchannell88
In summary, two identical wires, A & B, carrying currents in an electric circuit exert a force on each other due to their resistance per unit length, r, and length, L, with a distance of a between them. This force is an attractive force in the same direction as the current. To achieve maximum force, the length, L, should be determined using the equation F = (µ0 *E^2)/(2*pi*a*r^2*L), where µ0 is the permeability and pi is 3.141592...
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..

Last edited by a moderator:

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!

## 1. What is the force between two identical wires in a circuit?

The force between two identical wires in a circuit is known as the magnetic force. It is caused by the interaction of the magnetic fields produced by the current flowing through the wires. This force is attractive when the current flows in the same direction and repulsive when the current flows in opposite directions.

## 2. How is the force between the wires calculated?

The force between two wires in a circuit can be calculated using the equation F = (μ0 x I1 x I2 x L) / (2π x d), where μ0 is the permeability of free space, I1 and I2 are the currents in the two wires, L is the length of the wires, and d is the distance between the wires. This equation is known as the Biot-Savart law.

## 3. Does the force between the wires change if the current or distance is altered?

Yes, the force between two wires in a circuit is directly proportional to the current flowing through the wires and inversely proportional to the distance between the wires. This means that as the current or distance is altered, the force between the wires will also change.

## 4. What happens to the force between the wires when the direction of the current is reversed?

When the direction of the current in one of the wires is reversed, the force between the wires will also reverse. This means that an attractive force will become repulsive and vice versa.

## 5. Is the force between the wires affected by the material of the wires?

The force between two wires in a circuit is not affected by the material of the wires, as long as they have the same dimensions and carry the same current. The force is solely determined by the current and distance between the wires.

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