Straight wires carrying DC currents

[fisico30]

Straight wires carrying DC currents...

Dear Forum,

when will two straight wires, both carrying a DC current, not feel any mutual magnetic force?

What reciprocal orientation do they need to have? It looks to me that they will always feel a magnetic force if they are parallel, perpendicular or at any other angle, since they are immersed in each other B field which is not parallel to the wire direction...is that true?

But I have been told that if they are infinite and perpendicular, there will be no net force...
Why? Net force in the sense that there are two forces that oppose each other, or no force on either wire?

thanks,
fisico30

 

[roam]

I think the magnetic force depends on the direction of the current in each wire... if the wires are carrying currents in the same direction they attract each other, but if they carry currents in the opposite direction then the force between them is repulsive. So the net force depends on whether the currents are parallel or anti-parallel.

 

[Matterwave]

If you have 2 perpendicular wires, I believe there would be a torque trying to rotate them about the line which joins them.

 

[chrisbaird]

If two current carrying wires are perpendicular, then the total linear force on one wire will be zero, simply because all the linear forces on one half of the wire will be canceled by forces on the other half. But it will experience a total angular force (a net torque) trying to turn the one wire until it is parallel to the other wire. Draw a little diagram and use F = qv x B at several point along the wire and you can see this pretty quickly. This case is actually very similar to an electric motor with square loops of wire near the outside creating the field and square loops near the axis responding to the field. Each loop feels feels a net torque but no net linear force, so the motor turns.

 

[sardar]

Dear fisico30,

Thank you for your question. The interaction between two straight wires carrying DC currents is governed by the principles of electromagnetism. According to the Biot-Savart law, a current-carrying wire produces a magnetic field around it, and this field can exert a force on another current-carrying wire.

The magnitude and direction of this force depend on the relative orientation of the two wires. If the wires are parallel, then the magnetic fields around them will also be parallel, and there will be a repulsive or attractive force between them (depending on the direction of the currents). If the wires are perpendicular, then the magnetic fields will be perpendicular as well, and there will be no net force between them.

However, as you correctly pointed out, in most cases, the wires will not be perfectly parallel or perpendicular, and there will be some degree of interaction between them. This is because the magnetic field around a wire is not uniform and changes in strength and direction as you move away from the wire. Therefore, even if the wires are at an angle to each other, there will still be some component of the magnetic field that is parallel or perpendicular to the other wire's direction, resulting in a net force between them.

In the case of two infinite and perpendicular wires, the magnetic fields will be uniform and parallel to each other, resulting in equal and opposite forces that cancel each other out. This means that there will be no net force on either wire, and they will not experience any mutual magnetic force.

I hope this helps to clarify the concept. If you have any further questions, please don't hesitate to ask. Keep exploring the fascinating world of electromagnetism!

Best regards,