Question

A magnetic field of $B=5t^2$ exists in a cylindrical region as shown in figure. A conducting square loop of side $l=2cm$ is placed inside a cylinder such that one of the vertex of square is at the center of cylinder.

• A. EMF induced in side AB at t = 2 sec is 4 mV
• B. Potential difference developed in side OA at t = 2 sec is 2 mV
• C. Potential difference across side AB at t = 2 sec is 2 mV
• D. EMF induced across side OA at t = 2 sec is 2mV

Answer 1

Answer: (A), (B)

Potential difference developed in side OA at t = 2 sec is 2 mV

$\epsilon =\frac{d\varphi }{dt}=\frac{d}{dt}5t^2\times 4\times {10}^{-4}=4tmV$ [EMF of loop]
${\epsilon }_{OA}={\epsilon }_{OC}=0$ & ${\epsilon }_{AB}={\epsilon }_{BC}=\frac{\epsilon }{2}$
${\epsilon }_{AB}=4mv$ at t = 2