MAG - Forces on Current Carrying Wires

Forces on Current Carrying Wires

Magnetic Field Due to a Long Straight Wire

We've already discussed how a current carrying wire produces a magnetic field. Let's look into that further. The magnetic field loops around the wire. This can be verified by moving a compass around a wire and tracing the magnetic field. It can also be shown through experiment that the strength of the magnetic field decreases as you move away from the wire or if you decrease the current flowing through the wire. Mathematically we calculate the magnetic field strength by:

, where r is the distance from the wire to the point where you measure the field.

The constant μ0 is known as the permeability of free space. A material's magnetic permeability is a measurement of how well a magnetic field can form and remain supported in the material. Space has a relatively low permeability of

Non-ferromagnetic materials will have similar low permeabilities. This basically means a magnetic field will only exist in the material as long as it is being provided by an external source. Ferromagnetic materials have a significantly higher magnetic permeability. Once these materials have been exposed to an external magnetic field, they will retain that field to some degree even after the original source is removed.

Force Between Two Parallel Wires

A current carrying wire will experience a force when in an external magnetic field, regardless of what creates that field. For example if you ran two current carrying wires parallel to each other, their mutual magnetic fields would interact causing a force on each. Consider two parallel wires each with a current I flowing up, and separated by distance d. The magnitude of the field B1 at wire 2 is given by:

Therefore, the force exerted on wire 2 by wire 1's B field is:

For wire 2 the magnetic field due to wire 1 is pointing into the page. Using the right hand rule we see that the force F2 is pulling wire 2 towards the left.

You can show that the force acting on wire 1 must be equal and opposite to the force acting on wire 2, therefore it experiences a force F1 = F2 and to the right.

When the current in the two wires runs in the same direction, the wires experience an attractive force due to the magnetic field interaction.

What would happen if the currents where to flow in the opposite direction? Watch this video to find out.

When the wires are labeled as being in "series" that indicates that the current flows up through one wire then immediately down through the second, so the currents flow in opposite directions. For the wires in "parallel" the current flows to a junction and splits going up both wires in the same direction before recombining at the top of the wires.

Forces on Wires Practice

1. An electric wire carries a DC current of 25 A vertically up the wall of a building. What is the magnetic field due to this current at a point P located 10 cm to the right of the wire?

2. Two parallel straight wires 10.0 cm apart carry currents in opposite directions. Current I₁ = 5.0 A is vertically up. Current I₂ = 7.0 A is going vertically down. Determine the magnitude and direction of the field exactly half-way between the wires.

3. The two wires of a 2.0-m-long appliance cord are 3.0 mm apart and carry a current of 8.0 A DC. Calculate the force one wire exerts on the other.

SOLUTIONS Links to an external site.

Torque on a Current Loop

If you create a current loop and place it in an external magnetic field, the field inside the loop will interact with the external magnetic field. Consider the loop shown here. The side view shows that the current in the loop flows down the left side, around, and up the right side. Our right hand rule #1 modification tells us that the direction of the magnetic field due to the current in the loop is pointing out of the board. This loop has been created so that it can rotate about the axis shown. Looking at the top view we see that the current flowing into the page on the left side creates a force that would push that side down. The current flowing out of the page on the right side creates a force that would push that side up. When allowed to rotate, these forces combine to create a torque on the loop that will rotate it counter clockwise from our top view.

Note: The top and bottom of the loop don't contribute to the net torque because their forces point either up or down from the loop and cancel each other.

Remember from previous courses that a torque is applied when a force causes rotation. Notice that the rotation here will cause the magnetic field of the loop to align with the external magnetic field. Regardless of direction of current, the loop will always rotate so that these two magnetic fields align. The magnitude of the torque is proportional to the number of loops, the current, the area of the loop, and the strength of the external magnetic field.

The quantities of loop number, current strength, and loop area all combine to describe a property of the loop known as the magnetic dipole moment. This is a vector quantity that points in the direction of the loops magnetic field, perpendicular to the loop's face. The magnitude of the magnetic dipole moment determines the strength of the torque that will be applied to the loop. If the dipole moment is doubled, the torque acting on the loop will also be doubled.

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