Finding Field Direction from Induced Current

← Back to Problems
Electromagnetic Induction Beginner Electromagnetic induction

Source: High school physics (Chinese)

Problem Sets:

Electromagnetic induction

Problem

A movable conducting wire slides to the right with velocity $v$ along a rectangular circuit. A magnetic field is present in region $A$, to the left of the wire. As the wire moves, the induced current it produces is directed upward in the wire (as shown).

Determine the direction of the magnetic flux density $B$ in region $A$.
Problem image
$B$ in region $A$ is directed into the page.

The induced current in the moving wire is driven by the magnetic force on its charge carriers, $\vec{F} = q\vec{v}\times\vec{B}$. For the conventional current to flow upward in the wire, this force on the positive carriers must point upward. With $\vec{v}$ to the right, $\vec{v}\times\vec{B}$ points upward only if $\vec{B}$ is directed into the page. Equivalently, by Lenz's law: as the wire moves right the area of region $A$ grows, and an upward current in the wire circulates counterclockwise around region $A$, producing an out-of-page field that opposes an increasing into-page flux -- consistent with $B$ into the page.