$A$ 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 $V$.

Out of the following given loops, in which loop is the direction of the induced current from $a \rightarrow c \rightarrow b$?

$A$ conductor of $3 \ m$ in length is moving perpendicularly to a magnetic field of $10^{-3} \ T$ with a speed of $10^2 \ m/s$. The $e.m.f.$ produced across the ends of the conductor will be ........ $V$.

$A$ rod of length $l$ is rotating in the plane of the paper with an angular speed $\omega$ about one of its ends,which is at a distance $a$ from an infinitely long conducting wire carrying current $i$ inwards the plane of the paper. Find the induced $emf$ in the rod at the instant as shown in the figure.

$A$ thin strip $10\, cm$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5\, N/m$ (see figure). The assembly is kept in a uniform magnetic field of $0.1\, T$. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $e$ is $N$. If the mass of the strip is $50\, g$, its resistance $10\, \Omega$ and air drag is negligible, $N$ will be close to:

Consider the situation given in the figure. The wire $AB$ is slid on the fixed rails with a constant velocity $v$. If the wire $AB$ is replaced by a semicircular wire of the same length,the magnitude of the induced current will: