Biot-Savart law:

$\overline{)\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}{\mathbf{=}}\frac{{\mathbf{\mu}}_{\mathbf{0}}}{\mathbf{4}\mathbf{\pi}}{\mathbf{\int}}\frac{\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\times}\hat{\mathbf{r}}}{{\mathbf{r}}^{\mathbf{2}}}{\mathbf{d}}{\mathbf{q}}}$

Integrating Biot-Savart law:

$\begin{array}{rcl}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}& \mathbf{=}& \frac{{\mathbf{\mu}}_{\mathbf{0}}}{\mathbf{4}\mathbf{\pi}}\mathbf{\int}\frac{\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\times}\hat{\mathbf{r}}}{{\mathbf{r}}^{\mathbf{2}}}{\mathbf{dq}}\\ & \mathbf{=}& \frac{{\mathbf{\mu}}_{\mathbf{0}}}{\mathbf{4}\mathbf{\pi}}\frac{\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\times}\hat{\mathbf{r}}}{{\mathbf{r}}^{\mathbf{2}}}\mathbf{\int}{\mathbf{dq}}\\ & \mathbf{=}& \frac{{\mathbf{\mu}}_{\mathbf{0}}}{\mathbf{4}\mathbf{\pi}}\frac{\mathbf{q}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\times}\hat{\mathbf{r}}}{{\mathbf{r}}^{\mathbf{2}}}\end{array}$

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)

Which of the following expressions gives the magnetic field at the point due to the moving charge?

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