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 and $|\vec{B}|$ increases as $y$ increases. 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

The magnetic field $\vec{B}$ increasing with $y$ implies a change in the magnetic field along the $y$-axis. According to Ampère's law with Maxwell's addition, a changing magnetic field can induce a current density $\vec{J}$ perpendicular to both the direction of $\vec{B}$ and the gradient of $|\vec{B}|$. Thus, $\vec{J}$ points in the $-z$ direction.

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

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