An $emf$ of $0.08\,V$ is induced in a metal rod of length $10\,cm$ held normal to a uniform magnetic field of $0.4\,T$,when it moves with a velocity of .......... $m/s$.

$A$ conducting rod of length $L$ rotates with angular speed $\omega$ in a uniform magnetic field of induction $B$ which is perpendicular to its motion. The induced emf developed between the two ends of the rod is

Refer to the figure. The arm $PQ$ of the rectangular conductor is moved from $x=0$ outwards. The uniform magnetic field is perpendicular to the plane and extends from $x=0$ to $x=b$ and is zero for $x>b$. Only the arm $PQ$ possesses substantial resistance $r$. Consider the situation when the arm $PQ$ is pulled outwards from $x=0$ to $x=2b$ and is then moved back to $x=0$ with constant speed $v$. Obtain expressions for the flux,the induced emf,the force necessary to pull the arm,and the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

$A$ rectangular coil $ABCD$ is rotated in a uniform magnetic field with constant angular velocity $\omega$ about one of its diameters as shown in the figure. The induced $emf$ will be maximum when the plane of the coil is

The wing span of an aeroplane is $20$ $m$. It is flying in a field where the vertical component of the Earth's magnetic field is $5 \times 10^{-5} \, T$,with a velocity of $360 \, km/h$. The potential difference produced between the wing tips will be ....... $V$.

The magnitude of the earth's magnetic field at a place is $B_0$ and the angle of dip is $\delta$. $A$ horizontal conductor of length $l$ lying along the magnetic north-south moves eastwards with a velocity $v$. The emf induced across the conductor is