The Magnetic Piece

• Proton has a magnetic moment. Review magnetic interactions of currents in magnetic field
  

  $$d\vec{F} = I d\vec{\ell} \times \vec{B}\\$$ (2.1)

  
  

• Remember that the cross product of two vectors points in the direction perpendicular to the plan formed by the two vectors. Recall the right hand rule, and the way that a screw works.

• Consider the example of a circular current loop in a uniform magnetic field
  
  

• easy to see without doing integral (every $d\vec{\ell}$ is partnered by a $-d\vec{\ell}$ on the opposite side of the loop and $\vec{B}$ is same everywhere) that the net force on the current loop will be zero.

• Force is not whole story. There can be net torque on the loop.
  

  $$d\vec{N} = \vec{r} \times d\vec{F}\\$$ (2.2)

  
  

  
  
  
  
  
  
  
  

• Do integral over the current, can come up for the torque on any current distribution
  

  $$\vec{N} = \vec{\mu} \times \vec{B}\\$$ (2.3)

  
  
  Refer to $\mu$ as the magnetic moment.

• Note that if you do a little math (see HW), can find for any planar loop that
  

  $$\vec{\mu} = I A\, \hat{n} \\$$ (2.4)