XV.gimnazija, Zagreb,Croatia Möbius in physics XV.gimnazija, Zagreb,Croatia Vedrana Vlahović, Dalibor Žgela

Goal We will study the difference between the shape of induced magnetic field, resistance and induction rate of „Möbius“ elements and the ones with no Möbius twist Applying the Möbius twist, we presume, will create an electromagnet with the same magnetic poles on both sides and reduce induction rates of both Möbius elements

Building our coils Fig.1: Coils We made two coils, one by winding copper wire “normally“ around a plastic tube, and the other by winding it around a half of the tube in one direction and around the other half in the opposite direction.

Coils In that way, we've managed to change the direction of coil's cross-section vector. Produced coils are the same length, have the same number of loops and their cross-section surfaces are the same size . Fig.2:Coils

Building our resistors Fig.3: Resistors In addition, we've made two circle-shaped resistors, one of which contains Möbius twist. Between the aluminum bands our resistors consist of, a paper band is placed, which prevents contact among the pieces of aluminum. Bands we used to make our resistors were the same length and width, so that created resistors were of equal diameter.

Affect of the Möbius twist on coil’s magnetic field As the charge is moving through the coil, magnetic field is being induced, whose direction can be determined by the right hand rule. Connecting the Möbius coil into the circuit we got an electromagnet with same poles on both sides (Fig. 5). When the switch is off, both magnetic needles point to the Earth's magnetic north pole (Fig. 4). Fig.4: While the switch is off Fig. 5: While the switch is on

Affect of a Möbius twist on the resistor Fig.6: Measuring data Applying the Möbius twist on the resistor, we produced a Möbius resistor. If we connect it to an electrical circuit, we should get a resistor of reduced inducted magnetic field. Indeed, magnetic needle has deflected less from its „normal“ position in the test with Möbius resistor than in the test with non-Möbius resistor .

Results Preliminary readings have shown slight but noticeable differences between induction rates of elements with and without the Möbius twist. Fig.7: Measuring data

Conclusion Considering that preliminary data confirmed our assumptions, we've decided to construct elements which will allow us to examine that difference more thoroughly and to determine it quantitatively. Fig. 8: Our coil’s evolution

Sources Vujević, Application of the Möbius strip in electrical engineering, Energija, god. 56(2007), br. 6., str. 700-711 www.quantumbalancing.com/news/htsinglenodecoil.pdf