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

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is:

A constant magnetic field of $1 \mathrm{T}$ is applied in the $\mathrm{x}>0$ region. A metallic circular ring of radius $1 \mathrm{m}$ is moving with a constant velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$ along the $x$-axis. At $t=0 \mathrm{s}$, the centre $\mathrm{O}$ of the ring is at $\mathrm{x}=-1 \mathrm{m}$. What will be the value of the induced emf in the ring at $\mathrm{t}=1 \mathrm{s}$ ? (Assume the velocity of the ring does not change.)

A rod of length $2 \mathrm{m}$ slides with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ on a rectangular conducting frame as shown in figure. There exists a uniform magnetic field of $0.04 \mathrm{T}$ perpendicular to the plane of the figure. If the resistance of the rod is $3 \mathrm{\Omega }$. The current through the rod is

A thin strip $10 \mathrm{c}\mathrm{m}$ long is on a $\mathrm{U}$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5 \mathrm{N}\mathrm{ }{\mathrm{m}}^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of $0.1 \mathrm{T}.$ If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $\mathrm{e}$ is $\mathrm{N}$ . If the mass of the strip is $50$ grams, its resistance $10\mathrm{\Omega }$ and air drag negligible, $\mathrm{N}$ will be close to:

A square frame of side $10 \mathrm{cm}$ and a long straight wire carrying current $1 \mathrm{A}$ are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ (see figure). The e.m.f induced at the time the left arm of the frame is at $x=10 \mathrm{cm}$ from the wire is

As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity $v$ in a perpendicular direction from a very long straight conductor carrying a steady current $I$. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf: $E$induced in the loop vary with time $t ?$

A metallic rod of length $L$ is rotated with an angular speed of $\omega$ normal to a uniform magnetic field $B$ about an axis passing through one end of rod as shown in figure. The induced emf will be :

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A horizontal rod of length $L$ rotates about a vertical axis with a uniform angular velocity $\mathrm{\omega }$. A uniform magnetic field $B$ exists parallel to the axis of rotation. Then potential difference between the two ends of the rod is

Consider the situation given in figure. The wire $AB$ slides on the fixed rails with a constant velocity. If the wire $AB$ is replaced by a semicircular wire, the magnitude of the induced current will: