$A$ conducting wheel with four rods of length $l$,as shown in the figure,is rotating with angular velocity $\omega$ in a uniform magnetic field $B$. The induced potential difference between its center and rim will be

An aeroplane in which the distance between the tips of wings is $50 \ m$ is flying horizontally with a speed of $360 \ km/hr$ over a place where the vertical component of the Earth's magnetic field is $2.0 \times 10^{-4} \ Wb/m^2$. The potential difference between the tips of the wings would be $V$.

Two infinitely long conducting parallel rails are connected through a capacitor $C$ as shown in the figure. $A$ conductor of length $l$ is moved with constant speed $v_0$. Which of the following graphs truly depicts the variation of current through the conductor with time?

$A$ rectangular wire loop of sides $8 \;cm$ and $2 \;cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \;T$ directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 \;cm \,s^{-1}$ in a direction normal to the $(a)$ longer side,$(b)$ shorter side of the loop? For how long does the induced voltage last in each case?

If current $I$ is flowing in a closed circuit with total resistance $R$,the rate of production of heat energy in the loop as we pull it with a constant speed $V$ is ($L=$ length of conductor,$B=$ magnetic field).

$A$ straight wire of length $L$ is bent into a semicircle. It is moved in a uniform magnetic field with speed $v$ with its diameter perpendicular to the field. The induced emf between the ends of the wire is