Diagram for calculating torque and force on magnetic dipoles a and b, where: $m_a$ and $m_b$ are the magnetic dipole moments (A·m2), $\hat m_a$ and $\hat m_b$ are the unit vectors in directions of the dipole vectors, $\hat r$ is the unit vector along the direction from the centre of the a dipole to the centre of b dipole, $\vec r$ is the vector between the centres of a and b (m), $r$ is the distance between the centre of the dipoles (m), $\vec m_a$ and $\vec m_b$ are the dipole moment vectors (A·m2), $\vec d_a$ and $\vec d_b$ - infinitesimal vector of the paths a and b, respectively (m), $\vec R$ - vector from $\vec d_a$ to $\vec d_b$ (m).
The drawing was created after: Peter B. Landecker, Daniel D. Villani, Kar W. Yung, An analytic solution for the torque between two magnetic dipoles, Magnetic and Electrical Separation, Vol. 10, pp. 29-33
torque_force_2_dipoles_em.png
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