# Force per unit length acting on four parallel wires

• joeyc
In summary, there is an arrangement of four wires in cross section with a 30° angle and a distance of 5cm. Wires 2 and 4 carry a current of 10mA out of the page, while wire 3 carries a current of 25mA into the page. Using the equation F/L = (μoIaIb)/2πd, the resultant force per unit length on wire 1 is zero due to the other three wires. To determine the distance s between the origin and wire 3, we can look at the magnetic fields rather than the forces. Since the value of I1 is unknown, further calculations cannot be done.
joeyc

## Homework Statement

An arrangement of four wires, in cross section, with θ=30° and u=5cm. Wire 2 and wire 4 carry the same magnitude of current (I2=I4=10mA) directed out of the page. Wire 3 carries current I3=25mA directed into the page.

If the resultant force per unit length on wire 1 is zero due to the other three wires, determine s, the distance between the origin and wire 3. Write your final answer in centimeters.

## Homework Equations

F/L = (μoIaIb)/2πd

## The Attempt at a Solution

I try to equate F2/L + F3/L + F4/L =0
but now what's makes me confusing is I don't have the value of I1, so how should I continue it?

Look at the magnetic fields rather than the forces. The force on any current in wire 1 is due to the external magnetic field at its location.

## 1. What is the force per unit length acting on four parallel wires?

The force per unit length acting on four parallel wires is the force exerted on one unit length (usually measured in meters) of the wires due to the interaction between them. This force is caused by the magnetic fields created by the currents flowing through the wires.

## 2. How is the force per unit length calculated for four parallel wires?

The force per unit length is calculated using the formula F = (μ0*I1*I2*L)/(2π*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 them.

## 3. What is the direction of the force per unit length acting on four parallel wires?

The direction of the force per unit length depends on the direction of the currents in the wires. If the currents are flowing in the same direction, the force will be attractive (towards each other), and if the currents are flowing in opposite directions, the force will be repulsive (away from each other).

## 4. How does the distance between the wires affect the force per unit length?

The force per unit length is inversely proportional to the distance between the wires. This means that as the distance between the wires increases, the force per unit length decreases, and vice versa.

## 5. What is the significance of understanding the force per unit length acting on four parallel wires?

Understanding the force per unit length is important in various applications, such as designing circuits and electrical systems. It allows us to predict and control the forces between wires, which can impact the stability and efficiency of the system.

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