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Motion of a charge in a magnetic field

  1. Feb 8, 2009 #1
    A particle of charge q and mass m starts its motion from origin with u=a i.A uniform B=b/4 i + (sin 60)/2 j exists everywhere in space.Find the component of velocity in y direction when z coordinate of it becomes maximum

    Sir, if I find the magnetic force,Its component is 0 in Y direction.With no force acting in Y direction ,how come its velocity changes??

    then I thought that

    I'm missing one step:the force is in z direction initially but when it starts going in a circular motion then the x component of the field will cross with velocity and produce a force which has a component in y direction.
    plz help me!!!!!!!!!

    thanks in advance
     
  2. jcsd
  3. Feb 9, 2009 #2

    gabbagabbahey

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    Treat your velocity as some unknown function of time: [itex]\vec{u}(t)=u_x(t)\hat{i}+u_y(t)\hat{j}+u_z(t)\hat{k}[/itex]. Then use the expression for the magnetic field and the Lorentz force law to find the equation of motion for the particle. Then solve that differential equation for [itex]\vec{u}(t)[/itex] and plug in the initial condition [itex]\vec{u}(0)=a\hat{i}[/itex]. Finally, find where the maximum of the z-component occurs.
     
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