# Helical solenoid helix

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What happens to the magnetic field when the helix of a solenoid is, itself, bent into a larger helix shape?

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You may see it as a change in the radius and number of coils of the solenoid and do the corresponding adjustments to your equation.

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That's not what I mean.

For example:

If a long piece of thick iron wire, tightly wound with magnet wire along its entire length, is then coiled into a helix.

What would happen to the magnetic field when current was applied to the magnet wire?

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EDIT 2

Sorry misread question and did torus not helix - whoops

you get a magnetic field that follows the internal volume of the torus, is proportional to the Number of Turns of wire, the Current, and the permeability; and is inversely proportional to the distance from the centre of torus to your measurepoint

$B = \frac{\mu . I . N}{2\pi r}$

You can get to this equation using Ampere's law and choosing a surface connected to a ring of equal distance from the torus's centre - the I_pen is the number of loops times the current. The direction of the magnetic field can be seen by examining any single loop of wire and doing right hand corkscrew rule

Edited by imatfaal
making equation relative permeability not vacuum
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What did you mean by magnetic wire? i think you mean what happens if you coil a solenoid, into another solenoid? I don't think it would deviate much from the helix model though, if the radius of the original solenoid was very small, compared to the bigger solenoid

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Since the generated field is concentrated axially to each coil, the axis of the field will follow the axis of the coils. So if they are twisted into a helix then the field axis will take this shape on, if they are twisted into some other shape they will follow that.

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Agreed with Imatfaal: the induction is very similar to a torus , except when the pitch of the bigger helix is not much smaller than its radius, in which case one may take sqrt[p^2+(2pi*r)^2] instead of 2pi*r, and orient the induction accordingly.

N is taken per turn of the bigger helix.

Edited by Enthalpy
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Ok, I think that makes sense! Thank you kindly.

Mellinia - when I said 'magnet wire' I meant the colloquial name for copper wire with an insulative varnish coating, used in electromagnets, not magnetic wire. Sorry for the confusion!

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