# Magnetism Problem: Find Force Between 2 Current Wires

• mrjack
In summary, the problem involves two 1m long current carrying wires with a separation of 0.05m. One wire carries 2A and the other carries 3A. The formula for magnetic force on a current carrying wire is F = IlBsin(\vartheta), and the formula for interaction between two sources is \frac{F}{l} = \frac{\mu I _{1} I_{2}}{2\pi r}. The desired output is the magnitude and direction of the mutual force between the wires. The correct answer can be obtained by plugging the values into the second equation, but this only solves for magnitude.

## Homework Statement

Two 1m long current carrying wires are separated by 0.05m. One carries 2A and one carries 3A. What is the magnitude of the mutual force between them? In what direction does the force act on each wire?

## The Attempt at a Solution

I apologize for not following the policy but I'm not sure where to start. I already have the answer so I'm not looking for an answer, but just how to go about solving the problem. Any help would be appreciated.

Surely you must know something about magnetic force? Start by posting that, then we can take it from there...

Thanks for the reply. Sorry, I guess I gave the impression that I know nothing..

Yes, I know that the force on a current carrying wire is found by F = IlBsin($$\vartheta$$).

And I have that the formula for interaction between two sources is $$\frac{F}{l}$$ = $$\frac{\mu I _{1} I_{2}}{2\pi r}$$

I actually did just try plugging into that second equation but I can't seem to get the right answer. (Plus that would only solve magnitude)

## What is the formula for finding the force between two current-carrying wires?

The formula for finding the force between two current-carrying wires is F = (μ₀I₁I₂L)/(2πd), where μ₀ is the permeability of free space, I₁ and I₂ are the currents in the wires, L is the length of the wires, and d is the distance between the wires.

## How does the distance between the wires affect the force between them?

The force between two current-carrying wires is inversely proportional to the distance between the wires. This means that as the distance between the wires increases, the force decreases, and vice versa.

## Can the force between two current-carrying wires be attractive or repulsive?

The force between two current-carrying wires can be both attractive and repulsive, depending on the direction of the currents in the wires. If the currents are in the same direction, the force between them is attractive. If the currents are in opposite directions, the force between them is repulsive.

## How does the strength of the currents in the wires affect the force between them?

The force between two current-carrying wires is directly proportional to the strength of the currents in the wires. This means that as the currents increase, the force between them also increases, and vice versa.

## What is the role of permeability in the force between two current-carrying wires?

The permeability of free space, represented by μ₀, is a constant in the formula for the force between two current-carrying wires. It determines the strength of the force and is affected by the material between the wires. In a vacuum, the value of μ₀ is constant, but in other materials, it may vary and affect the force between the wires.