# Electromagnetism question -- Forces between two current carrying wires

• cutielollipop
In summary: The magnetic field from one wire interacts with the moving electrons in the other wire to cause the force (attractive or repulsive) between the wires.
cutielollipop
Homework Statement
State whether the magnetic fields around each wire are clockwise or counter-clockwise. Will the wires repel or attract each other
Relevant Equations
right-hand rule

Here is the question. I just wanted to confirm and see if I'm understanding the question clearly. For 3a) I said the first wire would have the magnetic field going in a counter clock wise direction and the second wire would have a magnetic field going in a clockwise direction using the right hand rule. However I don't know if the wires will repel or attract each other. I think they will repel since the magnetic fields are in opposite directions. Help would be kindly appreciated.

For b) I said there would be an upward force on the wire.

You are correct about the B-field directions for the wires. For the forces, have you learned the vector Lorentz Force yet? That's the easiest way to develop the intuition about the resulting forces between current carrying wires.

I learned about Lenz's Law if that's what you mean. But I don't know about the vector Lorentz Force.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html

The magnetic field from one wire interacts with the moving electrons in the other wire to cause the force (attractive or repulsive) between the wires.

Edit -- Remember that the charge ##q## of an electron is negative, since that affects the direction of the Lorentz Force on the moving charge.

I find it easiest to visualise the behaviour, which I do by thinking of the field lines as trying to broaden, repelling their neighbours, and to shrink in length.
If both sets are clockwise, they will cancel in the middle and the two sets connect up. You end up with a single set of field lines clockwise around both. Their shrinking in length will pull the wires together.
If one set is clockwise and the other anticlockwise they will be parallel and in the same direction in the middle. Broadening them pushes the wires apart.

berkeman said:
Edit -- Remember that the charge q of an electron is negative, since that affects the direction of the Lorentz Force on the moving charge.
With respect, this is an inopportune moment to worry about this. Positive currents and fictitious positive carriers get you where you want to go IMHO.

Also if you have two wires do not use your left hand for one and your right hand for the other. Do not inquire as to why I mention this.

hutchphd said:
With respect, this is an inopportune moment to worry about this. Positive currents and fictitious positive carriers get you where you want to go IMHO.
But, but, my brain doesn't work that way. Makes me dizzy to try to do that...

hutchphd said:
Also if you have two wires do not use your left hand for one and your right hand for the other. Do not inquire as to why I mention this.

haruspex said:
I find it easiest to visualise the behaviour, which I do by thinking of the field lines as trying to broaden, repelling their neighbours, and to shrink in length.
If both sets are clockwise, they will cancel in the middle and the two sets connect up. You end up with a single set of field lines clockwise around both. Their shrinking in length will pull the wires together.
If one set is clockwise and the other anticlockwise they will be parallel and in the same direction in the middle. Broadening them pushes the wires apart.
I have already memorized "same sign charges repel, opposite sign charges attract." If I want to bypass the right hand rule and ##~\mathbf{F}=I\mathbf{L}\times\mathbf{B}~##, I find it easier to memorize and use the rule "parallel currents do the opposite from charges, same direction attract, opposite direction repel."

I have seen students during tests writing with their right hand while using their left hand to figure out magnetic field directions, presumably to save time. Left-handed students have a definite advantage here.

Last edited:
Pushoam

## What is the force between two parallel current-carrying wires?

The force between two parallel current-carrying wires is given by Ampère's force law. If the currents are in the same direction, the wires attract each other. If the currents are in opposite directions, the wires repel each other. The magnitude of the force per unit length between two wires separated by a distance $$r$$ and carrying currents $$I_1$$ and $$I_2$$ is $$F/L = \mu_0 I_1 I_2 / (2 \pi r)$$, where $$\mu_0$$ is the permeability of free space.

## How does the distance between two current-carrying wires affect the force between them?

The force between two current-carrying wires is inversely proportional to the distance between them. As the distance $$r$$ increases, the force per unit length $$F/L$$ decreases according to the formula $$F/L = \mu_0 I_1 I_2 / (2 \pi r)$$. Conversely, as the distance decreases, the force increases.

## Why do two parallel wires carrying current in the same direction attract each other?

Two parallel wires carrying current in the same direction attract each other due to the magnetic fields they generate. Each wire creates a circular magnetic field around itself. According to the right-hand rule, if the currents are in the same direction, the magnetic fields between the wires interact in such a way that they produce an attractive force. This is a consequence of the Lorentz force acting on the moving charges in the wires.

## What happens if the currents in two parallel wires are in opposite directions?

If the currents in two parallel wires are in opposite directions, the wires repel each other. The magnetic fields generated by the wires interact such that the force between them is repulsive. This is because the magnetic field lines between the wires oppose each other, leading to a repulsive Lorentz force on the moving charges in the wires.

## How can the force between two current-carrying wires be measured experimentally?

The force between two current-carrying wires can be measured experimentally using a setup where the wires are suspended and allowed to move freely. By passing currents through the wires and measuring the displacement or force required to keep the wires at a certain distance, the force can be calculated. Sensitive force sensors or balance methods can be used to measure the small forces involved. The experimental results can then be compared to the theoretical prediction given by $$F/L = \mu_0 I_1 I_2 / (2 \pi r)$$.

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