$A$ cycle wheel of radius $0.5 \; m$ is rotated with a constant angular velocity of $10 \; rad/s$ in a region of magnetic field of $0.1 \; T$ which is perpendicular to the plane of the wheel. The $EMF$ generated between its centre and the rim is.....$V$

$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

$A$ long solenoid with $2000$ turns per meter has a small loop of radius $3 \,cm$ placed inside the solenoid normal to its axis. If the current through the solenoid increases steadily from $1.5 \,A$ to $5.5 \,A$ in $\frac{\pi^2}{100} \,s$, the induced emf in the loop is (in $\,mV$)

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 2\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\,\mu F$ is connected as shown in the figure. Then

$A$ 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 $B_{V} = 15 \mu T$)

The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. $A$ uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b$. Identify the graph showing the variation of different quantities with distance.