Question

In the given figure, O is the origin of a cylindrical region having magnetic field $B=B_{0}t$. OAB is an equilateral triangular loop of side L. Radius of the cylinder is R.

• A. EMF induced in side OA is $\frac{B_0\pi R^2}{18}$
• B. EMF induced in side OB is zero
• C. EMF induced in side AB is $\frac{B_0\pi R^2}{6}$
• D. EMF induced in side AB is $\frac{B_0\pi R^2}{18}$

Answer 1

Answer: (B), (C)

EMF induced in side AB is $\frac{B_0\pi R^2}{6}$

EMF induced in loop OAB is $|\epsilon |=\frac{d\varphi }{dt}=A\frac{dB}{dt}=\frac{\pi R^2}{6}\frac{d}{dt}{B}_{0}t$
$\Rightarrow$$\frac{B_0\pi R^2}{6}$
${\epsilon }_{OA}={\epsilon }_{OB}=0$; because, the induced field lines are perpendicular to $OA$ and $OB$.
$\therefore {\epsilon }_{AB}=\epsilon =\frac{B_0\pi R^2}{6}$