$A$ circular coil of area $3 \times 10^{-2} \, m^2$, $900$ turns, and a resistance of $1.8 \, \Omega$ is placed with its plane perpendicular to a uniform magnetic field of $3.5 \times 10^{-5} \, T$. The current induced in the coil when it is rotated through $180^{\circ}$ in half a second is (in $ \, mA$)

$A$ straight conductor of length $4 \,m$ moves at a speed of $10 \,m/s$. When the conductor makes an angle of $30^{\circ}$ with the direction of a magnetic field of induction $0.1 \,Wb/m^2$, the induced emf is: (in $\,V$)

$A$ conducting rod of length $l$ moves with velocity $\upsilon$ in a direction parallel to a long wire carrying a steady current $I$. The axis of the rod is maintained perpendicular to the wire with the near end at a distance $r$ away as shown in the figure. Find the emf induced in the rod.

$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $AO = l$ and $OC = 3l$. Then which of the following is incorrect?

An aeroplane having a wing span of $30 \ m$ flies due north with a speed of $170 \ m/s$. If the vertical component of the Earth's magnetic field is $B = 3.6 \times 10^{-5} \ T$, the potential difference between the tips of the wings will be: (in $mV$)

$A$ conducting rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\overrightarrow B$ at speed $v$ on two horizontal parallel ideal conductor rails. The ends of the rails are connected to a resistor $R$. The separation between the rails is $d$. The rod maintains a tilted angle $\theta$ to the rails. Find the external force required to keep the rod moving.