Force due to currents in parallel wires

In summary: This is why, when you are stationary with respect to the wires, you only perceive the attractive force between the wires. However, when you move with the charges, you are essentially moving with the magnetic field and the forces cancel out, leaving only the electrostatic repulsion between the charges. In summary, when observing charges in parallel wires, their motion and the observer's frame of reference play a crucial role in determining whether they will attract or repel.
  • #1
Knissp
75
0
Homework Statement

Two negative charges repel each other.
Two parallel wires with current going in the same direction attract each other.

Yet if one walks with the moving charge in the wires, the charges appear stationary and should repel each other - explain why if you are stationary with respect to the wire, they would attract while if you move with the charge they should repel."


The attempt at a solution
This is more of a conceptual question, so I really don't know how to approach it. Any help would be appreciated. I don't think the equations are relevant, but there's Coulomb's Law for static charges and the fact that currents going in the same direction in parallel wires attract, but I don't know how to resolve the issue of different frames of reference, i.e. the charges are stationary wrt the observer or the charges are moving wrt the observer and how this affects the force perceived.
 
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  • #2
Here's the gist: when you have stationary charges, the only force (apart from gravity) acting on them is the electrostatic force described by Coulomb's law. When you have a current, that force is still present, but there's a magnetic field around both the wires that causes the attractive force (according to the right-hand rule).

Now the magnetic force is stronger then the electrostatic force, as proven by the following equation between 2 parallel wires [tex]\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2 \pi d}[/tex].
Note that F (magnetic force) decreases at a rate of 1/d (distance between wires) while in Coulomb's law, the electrostatic force decreases as a function of 1/d^2, which means that the magnetic force will be much stronger, causing the attraction.
 
  • #3


I would first clarify that the statement "Two negative charges repel each other" is true for static charges, but when considering current-carrying wires, the force between the two wires is due to the interaction between the magnetic fields generated by the currents. This is known as the Lorentz force law.

Now, regarding the issue of different frames of reference, it is important to understand that the force between the two wires is dependent on the relative motion between them. If we are stationary with respect to the wires, we can observe the magnetic fields generated by the currents and see that they are interacting in a way that causes the wires to attract each other. However, if we are moving with the charges in the wires, we are also moving with the magnetic fields and therefore do not observe any interaction between the fields. This can lead to the perception that the charges are repelling each other.

In reality, the force between the wires remains the same regardless of the observer's frame of reference. It is simply a matter of perceiving the force differently based on the observed motion. This can be explained by the principle of relativity, which states that physical laws remain the same in all inertial frames of reference. Therefore, the force between the wires remains attractive in both frames of reference, but the perception of the force may differ.
 

What is the force due to currents in parallel wires?

The force due to currents in parallel wires, also known as the Lorentz force, is the force exerted on a wire when a current-carrying wire is placed near it. This force is the result of the interaction between the magnetic fields produced by the two wires.

How is the force due to currents in parallel wires calculated?

The force due to currents in parallel wires is calculated using the formula F = I1 * I2 * L / 2πd, where I1 and I2 are the currents in the two wires, L is the length of the wires, and d is the distance between them.

What factors affect the force due to currents in parallel wires?

The force due to currents in parallel wires is affected by the magnitude of the currents, the distance between the wires, and the length of the wires. Additionally, the direction of the currents and the magnetic field strength can also impact the force.

What is the direction of the force due to currents in parallel wires?

The direction of the force due to currents in parallel wires is perpendicular to both the direction of the magnetic field and the direction of the currents. This is known as the right-hand rule in physics.

What applications does the force due to currents in parallel wires have?

The force due to currents in parallel wires has many practical applications, such as in electric motors, speakers, and generators. It is also used in magnetic levitation technology, where the force between two parallel wires is used to suspend objects in mid-air.

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