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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Biot-Savart Law (Calculus) concept. You can view video lessons to learn Biot-Savart Law (Calculus). Or if you need more Biot-Savart Law (Calculus) practice, you can also practice Biot-Savart Law (Calculus) practice problems.