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Math Help - Motion of a particle in a magnetic field.

  1. #1
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    Motion of a particle in a magnetic field.

    The only force acting on a particle with charge e and velocity v, in a constant magnetic field B, is ev B. Also, r(0)=0 and \dot{\textbf{r}}(0)=\textbf{V}.

    I've shown that: m\dot{\textbf{r}}=e\textbf{r} \times \textbf{B} + m\textbf{V}.

    Now the question asks to find equations for the path of the particle if B=(B,0,0) , V=(v_1,v_2,0) and r=(x,y,z).

    I evaluated the cross product and equated the components to get:

    \dot{x}=v_1
    \dot{y}=\frac{eB}{m}z + v_2
    \dot{z}=\frac{eB}{m}y

    By solving the second and third equations, I generate equations involving exponentials but the answer has equations involving sin and cos.

    Can someone see where I've gone wrong? Thanks in advance.
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  2. #2
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    Quote Originally Posted by 0-) View Post
    The only force acting on a particle with charge e and velocity v, in a constant magnetic field B, is ev B. Also, r(0)=0 and \dot{\textbf{r}}(0)=\textbf{V}.

    I've shown that: m\dot{\textbf{r}}=e\textbf{r} \times \textbf{B} + m\textbf{V}.

    Now the question asks to find equations for the path of the particle if B=(B,0,0) , V=(v_1,v_2,0) and r=(x,y,z).

    I evaluated the cross product and equated the components to get:

    \dot{x}=v_1
    \dot{y}=\frac{eB}{m}z + v_2
    \dot{z}=\frac{eB}{m}y

    By solving the second and third equations, I generate equations involving exponentials but the answer has equations involving sin and cos.


    Can someone see where I've gone wrong? Thanks in advance.
    \dot{z} = {\color{red}-} \frac{eB}{m}y.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    \dot{z} = {\color{red}-} \frac{eB}{m}y.
    Of course! I can't believe I went through it twice and made the same mistake both times.

    Thank you for your help.
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