$A$ copper disc of radius $0.1 \ m$ is rotated about its centre with $10$ revolutions per second in a uniform magnetic field of $0.1 \ T$ with its plane perpendicular to the field. The e.m.f. induced across the radius of the disc is:

$A$ conducting rod is moving in a uniform magnetic field as shown in the diagram. Which end is at a lower potential?

$A$ coil of $N$ turns and mean cross-sectional area $A$ is rotating with uniform angular velocity $\omega$ about an axis at right angle to a uniform magnetic field $B$. The induced e.m.f. $E$ in the coil will be

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\vec{B}$ exists parallel to the axis of rotation. The $e.m.f.$ induced between two ends of the rod is

$A$ uniform magnetic field exists in a region given by $\vec B = 3\hat i + 4\hat j + 2\hat k \, T$. $A$ conducting rod of length $5\,m$ is placed along the $y$-axis and is moved along the $x$-axis with a constant speed of $1\,m/s$. The $emf$ induced in the rod will be......$V$.

$A$ conducting wire $XY$ of mass $m$ and negligible resistance slides smoothly on two parallel conducting wires as shown in the figure. The closed circuit has a resistance $R$ due to $AC$. $AB$ and $CD$ are perfect conductors. There is a magnetic field $\vec{B} = B(t) \hat{k}$.
$(i)$ Write down the equation for the acceleration of the wire $XY$.
$(ii)$ If $\vec{B}$ is independent of time,obtain $v(t)$,assuming $v(0) = u_0$.
$(iii)$ For $(ii)$,show that the decrease in kinetic energy of $XY$ equals the heat lost in $R$.