JEE Main 2010
- Exam
- JEE Main
- Year
- 2010
- Subject
- Physics
- Chapter
- Electromagnetic Induction
JEE Main 2010 · Physics · Electromagnetic Induction
A rectangular loop has a sliding connector PQ of length and...
A rectangular loop has a sliding connector PQ of length and resistance and it is moving with a speed as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents and are
Options
- A\mathrm{I}\mathrm{I}
- B\mathrm{I}\mathrm{I}
- C
- D
Correct answer
B. \mathrm{I}\mathrm{I}
Step-by-step solution
A moving conductor is equivalent to a battery of emf (motion emf)
Equivalent circuit
\mathrm{I}=\mathrm{l}}_{1}+ \mathrm{l}}_{2}
applying Kirchoff's law
\begin{aligned}& \mathrm{I}}_{1} R+I R-v B \ell=0 \\
& \mathrm{I}}_{2} R+I R-v B \ell=0
\end{aligned}adding (1) \& (2)
\begin{aligned}& 2 \mathrm{IR}+\mathrm{IR}=2 \mathrm{vB} \ell\\
& \mathrm{I}=\frac{2 \mathrm{vB} \ell}{3 \mathrm{R}}\\
& \mathrm{I}}_{1}= \mathrm{I}}_{2}=\frac{\mathrm{vB} \ell}{3 \mathrm{R}}
\end{aligned}