$A$ straight conductor of length $0.6 \, m$ is moved with a speed of $10 \, ms^{-1}$ perpendicular to a magnetic field of induction $1.2 \, Wb \cdot m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

The magnetic field in a region is given by $\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }$. $A$ square loop of side $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\overrightarrow{ v }= v _{0} \hat{ i }$. The emf induced in the loop is:

An aeroplane is travelling horizontally towards west with a speed of $540 \,km/h$. The wing span of the plane is $20 \,m$. If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$, the potential difference developed between the ends of the wing is (in $\,V$)

$A$ $1.0 \ m$ metallic rod is rotated with an angular frequency $200 \ rad \ s^{-1}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. $A$ constant and uniform magnetic field of $0.5 \ T$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is . . . . . . . (in $V$)

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

Two infinitely long conducting parallel rails are connected through a capacitor $C$ as shown in the figure. $A$ conductor of length $l$ is moved with constant speed $v_0$. Which of the following graphs truly depicts the variation of current through the conductor with time?