# Magnetic forces exerted by current-carrying wires

• SA32
In summary, the figure shows three long wires with linear mass density 50 g/m, carrying equal currents and arranged in an equilateral triangle. The lower two wires are 4.0 cm apart and attached to a table. To allow the upper wire to "float", it must be repelled by the two lower wires with a magnetic force equal and opposite to its weight. The force from each lower wire on the top wire can be determined by considering the vertical and horizontal components of the forces, and the mass of the upper wire can be calculated using the equation for magnetic force as F=I1LB2 and equating it to F=mg with "m" being the mass per unit length.

## Homework Statement

The figure (http://img.photobucket.com/albums/v80/northerndancer/thefigure.jpg?t=1173558797 [Broken]) is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to "float" so as to form an equilateral triangle with the lower wires?

## Homework Equations

F=I1LB2 (magnetic force between two parallel wires)
F=mg (force due to an object's weight)

## The Attempt at a Solution

The two bottom wires exert attractive magnetic forces on each other because they are parallel and both of their currents move in the same direction. In order for the third wire to "float", it must be repelled by the two lower wires by a magnetic force equal and opposite to its weight. But:

-The upper wire is not parallel to the lower wires, so I'm not sure how to calculate the force each lower wire exerts on the upper wire.
-How do I calculate the mass of the upper wire if I don't know its length?

Thanks for any hints.

Last edited by a moderator:
SA32 said:
In order for the third wire to "float", it must be repelled by the two lower wires by a magnetic force equal and opposite to its weight.
Good!

But:

-The upper wire is not parallel to the lower wires, so I'm not sure how to calculate the force each lower wire exerts on the upper wire.
Sure they are parallel. They are not in the same vertical line, but all three wires are parallel. What direction is the force from each lower wire on the top wire? Hint: Consider the vertical and horizontal components of those forces.
-How do I calculate the mass of the upper wire if I don't know its length?
Think in terms of force per unit length and mass per unit length.

Okay I think I see, the top wire is parallel to each of the bottom wires, just the force from each has both an x-component and y-component. But the x-components cancel out and so the net magnetic force on the top wire is just straight up, isn't it?

And looking again at the equation for the force between parallel wires, I think I get what you mean about the mass. The equation for magnetic force involves L, and then if I equate it to mg and make "m" = (50 g/m)*L the lengths should cancel out?

Exactly right.

## 1. What is a magnetic field?

A magnetic field is a region of space surrounding a magnet or a current-carrying wire where magnetic forces can be observed. It is created by the movement of electrically charged particles.

## 2. How are magnetic fields created by current-carrying wires?

When an electric current flows through a wire, it creates a circular magnetic field around the wire. The direction of the magnetic field is determined by the direction of the current flow, following the right-hand rule.

## 3. How do magnetic forces affect other objects?

Magnetic forces can exert a force on other magnetic objects or on charged particles. These forces can cause movement, attraction, or repulsion between the objects.

## 4. What is the relationship between current and magnetic field strength?

The strength of the magnetic field created by a current-carrying wire is directly proportional to the amount of current flowing through the wire. This means that as the current increases, the magnetic field strength also increases.

## 5. How can magnetic fields be used in everyday life?

Magnetic fields have many practical applications, such as in electric motors, generators, and MRI machines. They are also used in everyday objects like speakers, credit cards, and refrigerator magnets.