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 $\,V$)

$A$ metal wire $PQ$ slides on parallel metallic rails having separation $0.25 \ m$,each having negligible resistance. There is a $2 \ \Omega$ resistor and $10 \ V$ battery as shown in the figure. There is a uniform magnetic field directed into the plane of the paper of magnitude $0.5 \ T$. $A$ force of $0.5 \ N$ to the left is required to keep the wire $PQ$ moving with constant speed to the right. With what speed is the wire $PQ$ moving? ..... $m/s$ (Neglect self-inductance of the loop)

When a rod of length $l$ is rotated with angular velocity $\omega$ in a uniform magnetic field of induction $B$ perpendicular to the plane of rotation,about one of its ends,the induced emf across its ends is:

Two rails of a railway track,insulated from each other and the ground,are connected to a millivoltmeter. What is the reading of the voltmeter when a train travels with a speed of $180 \ km/hr$ along the track? Given that the vertical component of the Earth's magnetic field is $0.2 \times 10^{-4} \ Wb/m^2$ and the rails are separated by $1 \ m$.

$A$ 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:

$A$ rectangular loop $PQRS$ is being pulled with a constant speed into a uniform transverse magnetic field by a force $F$ (as shown). The $e.m.f.$ induced in side $PS$ and the potential difference between points $P$ and $S$ respectively are (Resistance of the loop $= r$)