Question

A magnetic field B = 2t T exist in a cylinderical region as shown in figure. A square loop of side l = 2cm is placed inside the cylinder; such that, one of its vertices is at center of the cylinder. EMF induced in side AB of the square is

• A. 0.8 mV
• B. 0 V
• C. 0.2 mV
• D. 0.4 mV

Answer 1

The correct option is D 0.4 mV

EMF in the loop is, $\epsilon =\frac{d\varphi }{dt}=\frac{d}{dt}BA=\frac{d}{dt}2t{l}^2$
$\Rightarrow \epsilon =2\times (2\times {10}^{-2}{)}^2=8\times {10}^{-4}=0.8mV$
Since, the induced electric field lines are perpendicular to the sides OA and OC, the voltage induced in them is zero, and from symmetry, the voltage induced across AB and BC is same. Therefore,
${\epsilon }_{AB}={\epsilon }_{BC}=\frac{\epsilon }{2}=0.4mV$
& ${\epsilon }_{OA}={\epsilon }_{OC}=0$