In a certain region of space, suppose that $B_{x}=C x, B_{y}=-2 C y$, and $B_{z}=C z$, where $C$ is a positive constant. Is the $z$ component of the current density in this region positive, negative, or zero?
A) Positive
B) Negative
C) Zero
D) This is impossible.

Question

Quizplus · Accepted Answer

The magnetic field components given do not directly determine the current density's direction without additional information, such as the presence of a magnetic source or the application of Ampère's law. However, the question seems to imply a misunderstanding of the relationship between magnetic fields and current densities. The components of the magnetic field alone, without further context (like the application of Maxwell's equations), do not provide enough information to deduce the direction of current density. Therefore, without additional context or information, we cannot determine the z component of the current density to be positive, negative, or zero based solely on the given magnetic field components.

In a Certain Region of Space, Suppose That Bx=Cx,By=−2CyB_{x}=C x, B_{y}=-2 C yBx​=Cx,By​=−2Cy

In a Certain Region of Space, Suppose That $B_{x}=C x, B_{y}=-2 C y$