$A$ simple pendulum with a bob of mass $m$ and a conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of the Earth's magnetic field in the direction perpendicular to the swing is $B$. The maximum e.m.f. induced across the pendulum is ($g=$ acceleration due to gravity).

$A$ rod of length $l$ is rotated with angular velocity $\omega$ about one of its ends,in a region perpendicular to a uniform magnetic field of induction $B$. The induced e.m.f. in the rod is:

$A$ circular wheel with $10$ spokes, with its plane vertical along East-West, is rotating about its natural axis with a uniform speed of $100$ revolutions per minute in the Earth's magnetic field. The radius of the wheel is $0.3 \, m$. If the $EMF$ induced between the centre of the wheel and the rim is $3 \pi \mu V$, what is the angle of dip at that place? (Vertical component of the Earth's magnetic field $B_{V} = 15 \mu T$)

An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is:

$A$ rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the $x$-axis with a constant velocity $v_0$ in the plane of the paper. At $t=0$,the right edge of the loop enters a region of length $3L$ where there is a uniform magnetic field $B$ into the plane of the paper,as shown in the figure. For sufficiently large $v_0$,the loop eventually crosses the region. Let $x$ be the location of the right edge of the loop. Let $v(x)$,$I(x)$,and $F(x)$ represent the velocity of the loop,current in the loop,and force on the loop,respectively,as a function of $x$. Counter-clockwise current is taken as positive. Which of the following schematic plot$(s)$ is(are) correct? (Ignore gravity)

The radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of $r_0 \ m s^{-1}$. If at any instant the radius of the loop is $r$,then the emf induced in the loop at that instant will be: