Question

A rectangular loop of dimensions $l$ and $w$ moves with a constant speed $v$ through a region containing a uniform magnetic field $B$ directed into the paper and extending a distance of $4w$. Which of the following figures correctly represents the variation of emf $(\varepsilon)$ with the position $(x)$ of the front end of the loop?
\includegraphics[width=0.5\linewidth]{13.jpeg} \includegraphics[width=0.8\linewidth]{13.1.jpeg}

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Hint:

Whenever a loop enters or exits a magnetic region, only one side contributes to induced emf, producing a step-like graph.

Answer 1

The Correct Option is C

Step 1: Use Faraday's law.
Induced emf = $B l v$ for a rod of length $l$ moving with velocity $v$ perpendicular to a magnetic field. Here the side of length $w$ cuts the magnetic flux, so magnitude = $B w v$.

Step 2: Analyse entry into field.
When the front of the loop enters the field region, only one vertical segment is cutting flux ⇒ emf = $+Bwv$.

Step 3: When the loop is fully inside.
Two opposite vertical sides cut equal flux in opposite directions ⇒ net emf = $0$.

Step 4: When the loop leaves the field.
Only the back segment cuts the flux ⇒ emf = $-Bwv$.

Step 5: Conclusion.
The emf–position graph must show: • +Bwv at entry • 0 while fully inside • –Bwv at exit This matches option (B).