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Force on Moving Charges in a Magnetic Field

  1. Aug 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider the example of a positive charge q moving in the xy plane with velocity [tex]\hat{v}[/tex] = vcos([tex]\theta[/tex])[tex]\hat{x}[/tex] + vsin([tex]\theta[/tex])[tex]\hat{y}[/tex] (i.e., with magnitude v at angle [tex]\theta[/tex] with respect to the x-axis). If the local magnetic field is in the +z direction, what is the direction of the magnetic force acting on the particle?
    Express the direction of the force in terms of [tex]\theta[/tex], as a linear combination of unit vectors, [tex]\hat{x}[/tex], [tex]\hat{y}[/tex], [tex]\hat{z}[/tex].


    2. Relevant equations
    Cross product.
    [tex]\vec{C}[/tex] = [tex]\vec{A}[/tex] X [tex]\vec{B}[/tex] = (AxBy - AyBx)[tex]\hat{z}[/tex] + (AyBz - AzBy)[tex]\hat{x}[/tex] + (AzBx - AxBz)[tex]\hat{y}[/tex]


    3. The attempt at a solution
    I don't know what to plug in, and overall am just confused as to what the formula means.

    Any explanation would be greatly appreciated!
     
  2. jcsd
  3. Aug 13, 2008 #2

    Defennder

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    Homework Helper

    You only need to to apply the equation for the Lorentz force here. What have you learnt about how to evaluate the cross product of two vectors?
     
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