## Straight Current-Carrying Wire

When a long, straight current-carrying wire is placed in a magnetic field, it'll experience a force proportional to the strength of the field, the amount of current, and the length of the wire. You can see how this plays out in this image:

Thus, the magnitude of the magnetic force on a current-carrying wire is given by:

The direction of the magnetic field can be found using the right-hand rule. To determine the direction, hold up your right hand (the left won't work!). Point your index finger in the direction of the current and your middle finger in the direction of the field. Your thumb will point in the direction of the magnetic force.

Let's look at an example. The wire shown is being levitated by a magnetic field. What is the magnitude and direction of the magnetic field necessary to levitate this wire?

First, determine what magnetic force must be exerted on the wire. If the wire is suspended in the air, there are two forces acting on it. There is the downward force of gravity and an upward force due to the magnetic field. Therefore, the magnetic force acting upward on the wire must be equal to the force of gravity acting downward.

Now, you can calculate the magnitude of the magnetic field required to exert this force, making sure to use the formula we explored earlier. To get the maximum force with the smallest magnetic field, the field should be perpendicular to the current direction.

Finally, use the right-hand rule to find the direction of the magnetic field. Use your right hand and point your index finger in the direction of the current (left) and your thumb in the direction of the force (up). Then, your middle finger will point in the direction that the field should be directed.

Finally, use the right-hand rule to find the direction of the magnetic field. Use your right hand and point your index finger in the direction of the current (left) and your thumb in the direction of the force (up), then your middle finger will point in the direction that the field should be directed. So, to levitate this current-carrying wire, you would need a 0.065 T magnetic field directed outward in the +*z* direction.

## Two Parallel Current-Carrying Wires

Now you know that a current carrying wire can both create a magnetic field and experience a force due to a magnetic field. So what do you think would happen if you put two current-carrying wires near each other and parallel?

Each wire creates a magnetic field that exerts a force on the other wire! This will cause the wires to either be attracted to each other or repelled from each other. If the current in the wires is in the same direction, then the wires will exert attractive forces on each other. However, if the current in one of the wires is in the opposite direction from the current in the other wire, then the wires will repel each other.

This equation includes the constant, the magnetic permeability of free space, abbreviated by the Greek letter mu. The value of this constant is:

1.26 x 10-6 T*m/A.

If two 1.0 m-long wires are 1 cm (0.01 m) apart and parallel to each other and both carry a current of 20 A in the positive *x* direction, what is the magnetic force exerted between them?

Because the wires carry a current in the same direction, the force will be attractive, and you can use the previous equation to calculate the magnitude of this force. As you can see, we have:

## Current Loops

What happens if you bend the straight wire into a loop? The different sides of the loop experience forces in different directions because the current is flowing in different directions. If the force is exerted upwards on one side of the loop, it will be exerted downward on the other side. This means that the net force on a current loop in a magnetic field will be zero. However, these forces can still create a torque which will cause the loop to rotate. In fact, this is the basis of how electric motors work!

## Lesson Summary

Let's take a moment or two to recap the important information that we've learned about understanding forces on current-carrying wires within magnetic fields. Simply put, **current-carrying wires** create magnetic fields, and they also experience a force when placed in a magnetic field.

For a long, straight wire in a magnetic field, the magnetic force exerted on it is given by the formula:

When two current-carrying wires are parallel to each other, they will exert magnetic forces on each other because they both create magnetic fields. If the wire is bent into a loop, the net force acting on it will be zero, but there may still be a torque that causes the wire to rotate.