Let the current density at all points in a certain region of space be $\vec{J}$. The magnetic field $\vec{B}$ in that region points in the $+x$ direction with $|\vec{B}|=$ constant. This implies that $\vec{J}$ in that region
A) points in the $+x$ direction.
B) points in the $-x$ direction.
C) points in the $+y$ direction.
D) points in the $-y$ direction.
E) points in the $+z$ direction.
F) points in the $-z$ direction.
G) is zero.

Question

Quizplus · Accepted Answer

Since the magnetic field $\vec{B}$ is constant and points in the $+x$ direction, the curl of $\vec{B}$ is zero. According to Ampère's law (in the absence of a changing electric field), $\nabla \times \vec{B} = \mu_0 \vec{J}$. Therefore, $\vec{J}$ must be zero.

Let the Current Density at All Points in a Certain J⃗\vec{J}J

Let the Current Density at All Points in a Certain $\vec{J}$