🧄Analysis of Forces and Torques on a Current Loop in a Uniform Magnetic Field

The total force on a closed current loop in a uniform magnetic field is always zero due to the canceling out of forces on opposing segments of the loop, but a non-zero torque acts on the loop, causing it to rotate until its magnetic dipole moment aligns with the magnetic field, with the torque's magnitude being directly proportional to the current flowing through the loop, and its direction described by the cross product $\tau=\mu \times B$, resulting in a maximum torque when the loop's plane is parallel to the magnetic field and zero when perpendicular, and the torque's effect is visually demonstrated by the Current slider.

🎬how a current-carrying loop behaves in a uniform magnetic field

The torque on a current-carrying loop, which causes it to rotate within a magnetic field, is directly proportional to the current flowing through the loop. This principle is visually demonstrated by the Current (I) slider. When you increase the current, the forces acting on the loop become stronger, creating a greater torque. This larger torque causes a higher angular acceleration, resulting in the loop rotating and aligning with the magnetic field much more quickly. Conversely, decreasing the current weakens the torque, causing the loop to rotate more slowly.

how a current-carrying loop behaves in a uniform magnetic field

🖊️Mathematical Proof

Analysis of Forces and Torques on a Current Loop in a Uniform Magnetic Field | Proof and Derivationviadean on Notion