$A$ ceiling fan having $3$ blades of length $80 \ cm$ each is rotating with an angular velocity of $1200 \ rpm$. The magnetic field of Earth in that region is $0.5 \ G$ and the angle of dip is $30^{\circ}$. The $EMF$ induced across the blades is $N \pi \times 10^{-5} \ V$. The value of $N$ is:

$A$ square loop of area $25 \ cm^2$ has a resistance of $10 \ \Omega$. The loop is placed in a uniform magnetic field of magnitude $40 \ T$. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1 \ s$ will be:

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

$A$ conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $V$. The $emf$ induced in the frame will be proportional to

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform magnetic field $B$ directed into the plane of the paper (See figure). If charge densities $\sigma_1$ and $\sigma_2$ are induced on the left and right surfaces,respectively,of the sheet,then (ignore fringe effects):

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 $\,V$)