I\'m having a major issue trying to work out where the resultant lorentz force m

Question

I'm having a major issue trying to work out where the resultant lorentz force might act when I have a wire coiled around a doughnut (toroid) shape.

Am I right in saying that there will be a resultant lorentz force acting to crush the doughnut because there will be a slightly denser magnetic field on the inside of the doughnut than on the outside?

In addition, am I right in saying that the wire wrapped around the doughnut will be trying to escape from the doughnut in all directions?

I don't know if this is a good enough description of what I am trying to understand, please let me know if you need more info.

Explanation / Answer

I believe you are substantially correct.

Consider two parallel wires. If a current in each is flowing in the same direction then the wires will be pulled together. If the currents are in opposition, then they will be pushed apart.

Imagine a close wound toroidal coil without a magnetic core. The current running down the inside of one turn is in the opposite direction to the same current running up the outside of the same turn, so that turn of wire will try to expand away from the core. Now consider two adjacent turns, they have parallel currents so they will attract each other.

The filamentary toroidal surface current will therefore try to make a toroid with a shorter magnetic path length, but a thicker section with a smaller hole in the centre.
Magnetostriction will cause the magnetic core to reduce it's axial circumference while increasing it's cross section. That is in sympathy with the windings.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.