$A$ boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} \text{ T}$ and is directed due north and horizontal. The boat carries a vertical aerial $2 \text{ m}$ long. If the speed of the boat is $1.5 \text{ m/s}$,calculate the magnitude of the induced $emf$ in the aerial wire in $mV$.

Two straight conducting rails form a right angle as shown below. $A$ conducting bar in contact with the rails starts at the vertex at time $t=0$ and moves with a constant velocity of $v=5 \ m \ s^{-1}$ along them. $A$ magnetic field with $B=0.1 \ T$ is directed out of the page. The absolute value of the emf induced in the circuit at time $t=4 \ s$ will be (in $V$)?

$A$ horizontal straight wire $10 \; m$ long extending from east to west is falling with a speed of $5.0 \; m \, s^{-1}$,at right angles to the horizontal component of the earth's magnetic field,$0.30 \times 10^{-4} \; Wb \, m^{-2}$.
$(a)$ What is the instantaneous value of the $emf$ induced in the wire?
$(b)$ What is the direction of the $emf$?
$(c)$ Which end of the wire is at the higher electrical potential?

$A$ thin semicircular conducting ring of radius $R$ is falling with its plane vertical in a horizontal magnetic induction $B$. At the position $MNQ$,the speed of the ring is $V$ and the potential difference developed across the ring is

$A$ $10\,m$ long horizontal wire extends from North-East to South-West. It is falling with a speed of $5.0\,m/s$,at right angles to the horizontal component of the earth's magnetic field,which is $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced $emf$ in the wire is:

$A$ rectangular loop with a sliding connector of length $10\, cm$ is situated in a uniform magnetic field perpendicular to the plane of the loop. The magnetic induction is $0.1\, T$ and the resistance of the connector is $1\, \Omega$. The sides $AB$ and $CD$ have resistances $2\, \Omega$ and $3\, \Omega$ respectively. Find the current in the connector during its motion with a constant velocity of $1\, m/s$.