>[!summary] If there is a magnetic moment, current carrying wire and magnetic field in different directions from one another, there will be a torque on the wire to align with the magnetic field. > Key equations: $\vec{\tau} = \vec{\mu_0} \times \vec{B}$ $\mu _0 = I\cdot A$ # Torque On a Current Wire When you have a current loop and magnet inside the loop with a magnetic field, the magnet moment ($\mu _0$ / m) created by the current will experience a torque $\begin{array}{c} \vec{\tau} = \vec{\mu_0} \times \vec{B} \\ \vec{\tau} = IBAsin(\theta) \\\\ \text{Imporant note:}\\ \mu _0 = I\cdot A \end{array}$ The amount of torque is dependent on the angle with the magnet moment and the magnetic field. Max when the angle is 90 degrees. ![[Pasted image 20250602183440.png]] >[!note] Explanation Torque caused by the magnetic field and magnetic moment It's zero when the angle is 0 or 180 ![[Pasted image 20250602183427.png]] >[!note] Explanation Three example of torque on a current carrying wire We call the **<u>green box</u>** **stable equilibrium** since moving the magnet a small amount away from the magnet field will bring it back (Low [[Magnetic Potential Energy]]) We call the **red box** **unstable equilibrium** since a small disturbance will move the magnet into the green case (High [[Magnetic Potential Energy]]) >[!bug] Why is there a magnetic moment due to a closed loop wire Due to an electric field inside a closed wire caused by special relativity and length contraction which in a our reference frames make a magnetic field (Read [[Magnetic Flux & Bending Current#How does this Happen]]) # Extra Resources For more information in understanding magnetic torque I found this [video helpful](https://www.youtube.com/watch?v=hJxCLn4HNQ4&ab_channel=KhanAcademyIndia-English) --- 📂 Want to see more structured notes like these? Help grow the project by [starring Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidan-MathMatter). ---