Analysis of Magnetic Field and Torque of Magnetic Gear With Rotor Copper Bar

Ferrofluid drop impacts and Rosensweig peak formation in a non-uniform magnetic field

“…2. A numerical model 28 for a uniformly magnetised cylinder of the same size agreed with the on-axis measurements for a magnetisation of M = 1.22/ μ 0 T. The accuracy of the model was reduced off-axis, likely because the magnet is not exactly uniformly magnetised. Repeat measurements carried out using the same magnet over a long time span (∼3 years) have revealed no significant change in the on-axis flux density.…”

Dual Coil Patterned Ultra‐Thin Silicon Film Enable by Double‐Sided Process

“…Also, $${k_{\rm{t}}} = \; - NA\frac{{dB}}{{dz}}$$ is the transduction factor that is later used to determine the feedback electromechanical force in Equation (). The axial( B z ) and radial( B ρ ) component of the magnetic flux density of a cylindrical magnet is each defined as, [ 35 ] $$\[{B_{\rm{z}}}(\rho ,z) = - \frac{{{B_r}}}{{4\pi }}\int\limits_{0}^{{2\pi }}{{\int\limits_{0}^{R}{{\left( {\frac{{r(z + L)}}{{{{\left( {{r^2} + {{(z + L)}^2} + {\rho ^2} - 2r\rho \cos \phi } \right)}^{3/2}}}} - \frac{{rz}}{{{{\left( {{r^2} + {z^2} + {\rho ^2} - 2r\rho \cos \phi } \right)}^{3/2}}}}} \right)drd\phi }}}}\]$$ …”