$A$ long solenoid with $2000$ turns per meter has a small loop of radius $3 \,cm$ placed inside the solenoid normal to its axis. If the current through the solenoid increases steadily from $1.5 \,A$ to $5.5 \,A$ in $\frac{\pi^2}{100} \,s$, the induced emf in the loop is (in $\,mV$)

Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time $t=0$,its left arm passes the origin,$O$. If for $t \geq 0$,the current in the loop is $I$ and the distance of its left arm from the origin is $x$,then $I$ versus $x$ graph will be

$A$ conducting ring of radius $R$ is placed in a uniform inward magnetic field $\vec B$ as shown. If the ring is moving with velocity $\vec v$ in its plane,the induced $emf$ across the arc $PQ$ will be:

$A$ conducting wire bent in the shape of a semicircle has length $L$ and moves in its plane with constant velocity $v$. $A$ uniform magnetic field $B$ exists in the direction perpendicular to the plane of the wire. The velocity makes an angle $45^{\circ}$ to the diameter joining the free ends,and the emf induced between the ends of the wire is $\Phi = \alpha(B v L)$. The value of the constant $\alpha$ is

$A$ conducting circular loop is placed in a uniform magnetic field of $0.4\,T$ with its plane perpendicular to the field. The radius of the loop starts expanding at a constant rate of $1\,mm/s$. The magnitude of the induced emf in the loop at an instant when the radius of the loop is $2\,cm$ will be $...........\,\mu V$.

The magnetic induction in the region between the pole faces of an electromagnet is $0.7 \ Wb/m^2$. The induced $e.m.f.$ in a straight conductor $10 \ cm$ long,moving perpendicular to the magnetic field with a velocity of $2 \ m/s$ (where the conductor is also perpendicular to the field and its velocity),is.......$V$.