A conducting circular coil is place in a uniform magnetic field with the magnetic field initially directed perpendicular to the plane of the coil. In step $A$, the coil is rotated from its initial position by $60^{\circ}$ about its diameter in time $t$. In step $B$, the coil is further rotated about the same axis in the same sense by another $120^{\circ}$ in time $2 t$. Ratio of emf induced in the coil in step $A$ to that in step $B$ is

An aeroplane is travelling horizontally towards west with a speed of $540 \mathrm{kmh}^{-1}$. The wing span of the plane is 20 m . If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \mathrm{~T}$ and the dip angle is $30^{\circ}$, the potential difference developed between the ends of the wing is

If the vertical component of earth's magnetic field is $0.5 \times 10^{-4} \mathrm{~T}$ at a point. When an aeroplane of wing span 4 m is moving horizontally at this place at $360 \mathrm{kmh}^{-1}$, then the motional emf forced across the ends of the wings is

A boy is playing with the empty rim of a cycle wheel of radius 40 cm by rolling it along a horizontal road towards north with angular speed of $20 \mathrm{rad} \mathrm{s}^{-1}$. Considering the effect of magnetic field of earth, the e.m.f induced in the rim is

(Horizontal component of earth's magnetic field $=0.26 \mathrm{G}$ )