Magnetic Field and Magnetic Forces

  • Magnetic forces: \vec{F}=q\vec{v}\times\vec{B}.
  • Gauss’s law for magnetism: \oint\vec{B}\cdot d\vec{A}=0.
  • Magnetic force on a conductor: d\vec{F}=Id\vec{l}\times\vec{B}.
  • Magnetic torque: \vec{\tau}=\vec{\mu}\times\vec{B}, \vec{\mu}=I\vec{A}.  U=-\vec{\mu}\cdot\vec{B}.
  • Magnetic field of a moving charge: \vec{B}=\frac{\mu_0}{4\pi}\frac{q\vec{v}\times\hat{\vec{r}}}{r^2}.
  • The law of Biot and Savart: d\vec{B}=\frac{\mu_0}{4\pi}\frac{Id\vec{l}\times\hat{\vec{r}}}{r^2}.
  • Magnetic field of a long, straight, current-carrying conductors: \vec{B}=\frac{\mu_0 I}{2\pi r}.
  • Magnetic force between two long, parallel, current-carrying conductors: \frac{F}{L}=\frac{\mu_0 I I\prime}{2\pi r}.
  • Magnetic field at the center of a current loop: B=\frac{\mu_0 I}{2r}.
  • Long solenoid that has n turns per unit length: B=\mu_0 n I.
  • Ampere’s law: \oint\vec{B}\cdot d\vec{l}=\mu_0 I_{encl}.
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