Q. The magnetic field in the cylindrical region shown in figure increases at a constant rate of $20\ mT/sec$. Each side of the square lop $ABCD$ has a length of $1\ cm$ and resistance of $4\Omega$. Find the current in the wire $AB$ if the switch $S$ is closed
A) $1.25 \times 10^{- 7}\ A,$ (anti-clockwise)
B) $1.25 \times 10^{- 7}\ A,$ (clockwise)
C) $2.5 \times 10^{- 7}\ A,$ (anti-clockwise)
D) $2.5 \times 10^{- 7}\ A,$ (clockwise)
Explanation
(a) $i = \frac{e}{R} = \frac{A}{R}.\frac{dB}{dt} = \frac{\left( 1 \times 10^{- 2} \right)^{2}}{16} \times 20 \times 10^{- 3} = 1.25 \times 10^{- 7}A$
(Anti-clockwise)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.