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Electricity and Magnetism

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Maxwell's Equations: Current Density from Magnetic Field

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There exists a static magnetic field in free space given by the equation:

$$\vec{B}(xyz)=B_o \, xyz \, \hat{x}$$

What is the correct expression for the current density in this volume?

A

$\vec{J} = \cfrac{B_o}{\mu_o} \bigg(\hat{y}(xyz) + \hat{z} (xyz)\bigg)$

B

$\vec{J} = \cfrac{B_o}{\mu_o} \bigg(\hat{y}(xy) + \hat{z} (xz)\bigg)$

C

$\vec{J} = \cfrac{B_o}{\mu_o} \hat{x}(xy)$

D

$\vec{J} = B_o\bigg(\hat{y}(xy) + \hat{z} (xz)\bigg)$