Biot-Savart Law with Calculus Video Lessons

Concept

# Problem: Magnetic Field near a Moving ChargeA 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 µ0, q, v, x1, y1, and z1, and use x^, y^, and z^ for the three-unit vectors.

###### FREE Expert Solution

Magnetic field:

$\mathbf{|}{\mathbit{r}}_{\mathbf{3}}\mathbf{|}\mathbf{=}\sqrt{{{\mathbf{x}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{z}}_{\mathbf{1}}}^{\mathbf{2}}}$

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###### Problem Details

Magnetic Field near a Moving Charge

A particle with positive charge q is moving with speed 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 µ0, q, v, x1, y1, and z1, and use x^, y^, and z^ for the three-unit vectors.