The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \ T$ and the dip is $\tan^{-1}(4/3)$. $A$ thin metal rod of length $0.25 \ m$ placed in the north-south position is moved at a constant speed of $10 \ cm/s$ towards the east. Find the $e.m.f.$ induced in the rod across its ends in $\mu V$.

$A$ rod of length $l$,mass $m$,and resistance $R$ slides without friction down parallel conducting rails as shown in the figure. The rails are connected together at the bottom. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform vertical magnetic field $B$ exists throughout the region. Then the induced $emf$ in the loop,at the time the rod slides down with a speed $v$,is

Two parallel rails of a railway track, insulated from each other and from the ground, are connected to a millivoltmeter. The distance between the rails is $1 \, m$. $A$ train is travelling with a velocity of $72 \, km/h$ along the track. What is the reading of the millivoltmeter (in $mV$)? (The vertical component of the Earth's magnetic induction is $2 \times 10^{-5} \, T$.)

$A$ conducting rod $AB$ moves parallel to the $X-$ axis in a uniform magnetic field,which is directed perpendicular to the plane of motion (outwards). The end $A$ of the rod gets:

An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is:

$A$ very small circular loop of radius $a$ is initially (at $t=0$) coplanar and concentric with a much larger fixed circular loop of radius $b$. $A$ constant current $I$ flows in the larger loop. The smaller loop is rotated with a constant angular speed $\omega$ about the common diameter. The emf induced in the smaller loop as a function of time $t$ is