Question

A uniform resistive rod 'AB' of length $3m$ is sliding with a constant velocity of $2m/s$ on two long horizontal parallel rails of negligible resistance separated by 2 $m$. The resistance of rod 'AB' is $3\Omega$. The rails are connected with $6\Omega$ resistance. A uniform vertical magnetic field $2T$ exists as shown. Then, the correct statement(s) is/are

• A. Emf induced between the ends of the rod is $12V$
• B. Emf induced between the ends of the rod is $10V$
• C. Potential difference between the ends of the rod is $10V$
• D. Potential difference between the ends of the rod is $8V$

Answer 1

Answer: (A), (D)

The correct options are
A Emf induced between the ends of the rod is $12V$
D Potential difference between the ends of the rod is $8V$

$v=2m/s,B=2T,l=3m$
emf induced, $ϵ=Blv=2\times 3\times 2=12V$
The circuit becomes
Hence, $I=\frac{12}{9}=\frac{4}{3}A$

Potential difference across $AB=12-\frac{4}{3}\times 3$
$=12-4$ = $8V$