Magnetic field:

$\overline{)\begin{array}{rcl}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}& {\mathbf{=}}& \frac{{\mathbf{\mu}}_{\mathbf{0}}}{\mathbf{4}\mathbf{\pi}}\frac{\mathbf{q}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{}\mathbf{\times}\mathbf{}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{r}}}{{\mathbf{r}}^{\mathbf{3}}}\end{array}}$

**$\mathbf{\left|}{\mathit{r}}_{\mathbf{3}}\mathbf{\right|}\mathbf{=}\sqrt{{{\mathbf{x}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{z}}_{\mathbf{1}}}^{\mathbf{2}}}$**

Magnetic Field near a Moving Charge

A particle with positive charge *q* is moving with speed *v *along the *z* axis toward positive *z*. At the time of this problem it is located at the origin, *x*=*y*=*z*=0. Your task is to find the magnetic field at various locations in the three-dimensional space around the moving charge. (Figure 1)

Find the magnetic field at the point .

Express your answer in terms of *µ*_{0}, *q*, *v*, *x*1, *y*1, and *z*1, and use x^, y^, and z^ for the three-unit vectors.

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