Two parallel wires each carrying a current in opposite directions will _______

A pair of parallel wires serves to illustrate a principle that French scientist André-Marie Ampère was the first to comprehend, back in 1820.

The first person to discover evidence that electricity and magnetism are related phenomena was Hans Christian Ørsted. In the midst of a lecture on electricity, Ørsted noticed that a wire carrying current was able to deflect a compass needle. Unable to develop a plausible explanation, Ørsted published his findings in 1820. This news sent shockwaves through the scientific community and instigated numerous investigations into the matter. One of the scientists who immediately began to expand upon Ørsted’s work was Frenchman André-Marie Ampère. Soon after, Ampère found that the magnetic fields created by parallel current-carrying wires interact with one another, as demonstrated in this tutorial.

The direct current circuit in this tutorial includes two parallel straight wires (in red). These wires can be arranged in a series circuit, as they are when this tutorial first opens, or in a parallel circuit. In the series circuit arrangement, the parallel wires are linked by a connecting wire into a circuit that allows current along a single path. As a result, the current travels one way down one wire, and in the opposite direction down the second wire.

You can change this to a parallel circuit by clicking on the radio button; in this scenario, the current forks when it reaches the parallel wires; some current goes down one of the wires, the rest down the second. The current down both wires travels in the same direction.

Watch how the parallel wires behave in each of these set-ups. When either circuit type is selected, the Knife Switch can be lowered to complete the circuit by clicking either the switch itself or the blue Run button. Notice a stream of yellow electrons traveling through the circuit; flowing (as they always do) from negative to positive – opposite the direction of conventional current. To halt the flow of current, click on the red Stop button or the knife switch. Clicking the blue Pause button will let you examine the process in mid-stream.

As you can see, the wires in the series circuit repel one another, while the wires in the parallel circuit attract one another.

This is explained by the right hand rule, which helps visualize how a magnetic field (depicted by the blue field lines above) around a wire travels. Extend your thumb in the direction of the conventional current, then allow your fingers to curve: The magnetic field circling the wire (represented by your thumb) travels in the direction that your curved fingers are pointing.

So if you have two current-carrying, parallel wires with magnetic fields circling around them in the same direction, they will attract each other, as shown in the tutorial; at the point at which their respective magnetic fields intersect, they are traveling in opposite directions, and opposites attract.

Similarly, if you have two parallel wires with current traveling in opposite directions, as you do in the series circuit, then the magnetic fields of the two wires will be traveling in the same direction at the point at which they intersect, and therefore repel each other.

Ampère was able to mathematically describe this type of magnetic force between electric currents, formulating what is known as Ampère’s law.

Forces Between Parallel Conductors – Learn

When a wire has a current flowing through it a magnetic field will result around the wire. The magnetic field forms circular loops around the wire which decrease in strength as the distance from the wire increases. The direction of the magnetic field is determined using the right hand grip rule:

wrap fingers around the current carrying conductor
thumb points in the direction that the current flows
fingers indicate the direction of the magnetic field (often described as clockwise or anticlockwise depending on the view)

Two Current Carrying Conductors

When two wires carrying a current are placed parallel to each other, their magnetic fields will interact, resulting in a force acting between the wires. The magnitude of the force acting on each wire is equal, but the directions are opposite. This is true even if the conductors carry currents of different magnitudes.

The diagram below illustrates two examples where the direction of the magnetic field around each wire is drawn with the • × notation. Diagram A shows the current in the wires travelling in the same direction and diagram B shows the current travelling in opposite directions:

Determining the direction of the force

The direction of the force is determined by looking at the direction of the individual fields in the area between the conductors:

Diagram A: fields are opposite resulting in an attractive force
Diagram B: fields are the same resulting in a repulsive force

As a rule; when the current flowing through the conductors is in the same direction the force will be attractive and when the currents are opposite in direction the force will be repulsive.

Determining the magnitude of the force between two parallel conductors

The magnitude of the force acting between two parallel current carrying conductors is impacted by several factors:

The current in each conductor
The length of the conductors
The distance separating the conductors

The magnitude of the force acting between two parallel current carrying conductors is calculated using:

Where:

is the force per unit length between the conductors (in Nm−1)

is the magnetic permeability of free space (4π × 10−7 NA−2)*

is the current in wire 1 (in A)

is the current in wire 2 (in A)

is the distance separating the conductors (in m)

*note:

and

The equation can be written:

where

SI definition for electrical current; the ampere and Newton’s Third Law of Motion

The System International (SI) of Units states that the ampere is the unit for electrical current. The formal definition of the ampere is: One ampere is the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in a vacuum, would produce between those conductors a force equal to 2 × 10−7 N/m of length.

This is an application of Newton’s Third Law of Motion, which states: In a two-body system, if body A exerts a force on body B, then body B exerts a force on body A that is equal in magnitude, but opposite in direction.

Newton’s Third Law of Motion is sometimes stated: For every action there is an equal and opposite reaction. If one wire applies a force to a second wire, the second wire will apply a force that is equal in magnitude and opposite in direction on the first wire.

Example 1:

Two conducting wires, A and B, have currents flowing through them in different directions and are separated by a distance of 4cm. What is the magnitude and direction of the force per unit length acting between the wires if conductor A has a current of 2.5 A and conductor B has a current of 1.5 A?

Using:

Where: