$A$ metal rod of length $1\,m$ is rotated about one of its ends in a plane at right angles to a magnetic field of induction $2.5 \times 10^{-3}\,Wb/m^2$. If it makes $1800\,rpm$,calculate the induced e.m.f. between its ends in $V$.

In the given arrangement,a loop of width $b$ is moved with constant velocity $v$ through a uniform magnetic field $B$ restricted to a region of width $a$ (where $b > a$). The total time for which an $emf$ is induced in the circuit is:

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the potential of the points $P, Q$ and $R$.

$A$ rectangular loop circuit has a sliding wire $PQ$ as shown in the figure. The loop is placed in a magnetic field $B$,perpendicular to its plane. The resistance of the wire $PQ$ is $R$. If the wire moves with constant velocity $v$,then find the current flowing in the wire $PQ$?

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 $V$.

$A$ conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure. Two resistors $R_{1}$ and $R_{2}$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$. The correct statement about the directions of induced currents $I_{1}$ and $I_{2}$ flowing through $R_{1}$ and $R_{2}$ respectively is: