Magnetic Force

What is a magnetic field/force

• its a field that magnets produce and moving current also produces it :)

• Magnetic field and force can be described by the definition

  • ${\vec{F}}_m=q\vec{v}\times \vec{B}$
    • where $\vec{B}$ is electric field
    • and $\vec{v}$ is velocity
  • To find $\vec{B}$ we can use (this is the Biot-Savart Law)
    • $d\vec{B}=\frac{{\mu }_{0}I}{4\pi }\frac{d\vec{s}\times \hat{r}}{r^2}$

Magnetic Force on a current

• Force on a moving charge is:

  • ${\vec{F}}_m=q\vec{v}\times \vec{B}$
    • But this doesnt really work for current as current is moving charges
      • We can see that all charges are defined as the Length times the current
  • ${\vec{F}}_m=IL$

• Force is indpendent of shape and current

  • we just try to find all the length then find the hight diffrence
  • 
    • ALL of the horizontal component doesn’t matter ONLY the vertical (field has to be orthogonal)

• Force in a loop

  • if a current is in a loop in side a magnetic field the FORCE IS 0
    • 
      • if you add the in and out force it is zero but both of them make it spine because of the torque
        • $\vec{\tau }=\vec{R}\times \vec{F}$
      • The torque is different