Editing Nanorobotics (section)

===Movement of magnetic helical nanorobots===

One approach to the wireless manipulation of helical swimmers is through externally applied gradient rotation magnetic field. This can be done through Helmholtz coil as the helical swimmers are actuated by a rotating magnetic field. All magnetized objects within an externally imposed magnetic field will have both forces and torques exerted on them. The helical swimmers can rotate due the magnetic field received by the magnetic head and the forces acting upon it. Once the whole structure feels the field then the helical shape of its body converts this rotational movement into a propulsive force. Magnetic forces (fm) are proportional to the gradient of the magnetic field (∇B) on the magnetized object, and act to move the object to local maxima. Also, magnetic torques (τ) are proportional to the magnetic field (B) and act to align the internal magnetization of an object (M) with the field. The equations that express the interactions are as follows where V is the volume of the magnetized object.<ref>{{Cite journal |last1=Chesnitskiy |first1=Anton V. |last2=Gayduk |first2=Alexey E. |last3=Seleznev |first3=Vladimir A. |last4=Prinz |first4=Victor Ya |date=2022-11-04 |title=Bio-Inspired Micro- and Nanorobotics Driven by Magnetic Field |journal=Materials |volume=15 |issue=21 |pages=7781 |doi=10.3390/ma15217781 |doi-access=free |pmid=36363368 |issn=1996-1944|pmc=9653604 |bibcode=2022Mate...15.7781C }}</ref>

<math>\boldsymbol{F} = V \cdot (\boldsymbol{M} \cdot \nabla \boldsymbol{B})</math> (Equation 1)

<math>\boldsymbol{\tau} = V \cdot (\boldsymbol{M} \boldsymbol{\times} \boldsymbol{B})</math> (Equation 2)

Equation one indicates that, increasing the volume of the magnetic material will increase the force experienced by the material proportionally. If the volume is doubled, the force will also double, assuming the magnetization (M) and the gradient of the magnetic field (∇B) remain constant. This would be the same for the torque of the magnetic material too since it is proportional to the volume.

This increase in magnetic dipoles enhances the overall magnetic response of the material to an external magnetic field, resulting in greater force and torque. Hence when the magnetic material gets bigger than the helical swimmer it can move faster.