Question

The four wire loops shown in figure have vertical edge lengths of either $L,2L$ or $3L$. They will move with the same speed into a region of uniform magnetic field $\overrightarrow{B}$ directed out of the page. Rank them according to the maximum magnitude of the induced emf greatest to least.

• A. $1$ and $2$ tie, then $3$ and $4$ tie
• B. $3$ and $4$ tie, then $1$ and $2$ tie
• C. $4,2,3,1$
• D. $4$ then $2$ and $3$ tie, and then $1$
• E. answer required

Answer 1

Answer: (D)

$4$ then $2$ and $3$ tie, and then $1$

EMF induced on one edge perpendicular to the direction of motion and the direction of field is $Blv$
$l$ is the length of the edge.
Therefore emf will be greater for the side with greater length as the field $B$ and the velocity $v$ are the same for all
therefore,
emf 4>emf 2 > emf 2 >emf 1