🎬Visualizing Force and Torque on a Magnetic Dipole

The visualization dynamically demonstrates the magnetic torque equation, $M=m \times B$, and the resulting rotational dynamics of a current-carrying loop in a uniform magnetic field. By calculating the torque as a cross-product between the loop's magnetic moment ( $m$, blue vector) and the external magnetic field ( $B$, red vector), the simulation visually confirms the geometrical relationship: the torque vector ( $M$, green vector) is always perpendicular to the plane containing both $m$ and $B$. Crucially, the non-zero torque initiates an angular acceleration, causing the loop to physically rotate towards a state of minimum potential energy. The magnitude of $M$ varies sinusoidally, becoming maximal when $m$ is perpendicular to $B$ ( $\theta=90^{\circ}$ ) and dropping to zero when $m$ aligns with $B\left(\theta=0^{\circ}\right.$ or $\left.180^{\circ}\right)$, thereby defining the equilibrium position where the rotation ceases and minimum potential energy is achieved.

🎬Narrated Video

🧵Related Derivation

🧄Analysis of Forces and Torques on a Current Loop in a Uniform Magnetic Field (FT-CL-UMF)

⚒️Compound Page

Visualizing Force and Torque on a Magnetic Dipole | Resulmationviadean on Notion