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Electricity and Magnetism

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Maxwell's Equations: Divergence of the Magnetic Field

EANDM-HS1IXE

Consider these two vector fields:

$\vec{S}(x,y,z)=V_o(x\,\hat{x} + y\,\hat{y} + z\,\hat{z})$

$\vec{R}(x,y,z)=V_o(x\,\hat{x} + y\,\hat{y} - 2z\,\hat{z})$

These two vector fields are purported to represent a magnetic field in free space.

Of the four possible choices, which combination of answers is correct ('yes' means the vector field could represent a magnetic field, while 'no' means that it could not)

A

$\vec{S}$ yes
$\vec{R}$ yes

B

$\vec{S}$ yes
$\vec{R}$ no

C

$\vec{S}$ no
$\vec{R}$ yes

D

$\vec{S}$ no
$\vec{R}$ no