Production of Induced EMF

A jet plane is travelling towards wets at a speed of $1800 \mathrm{km} {\mathrm{h}}^{-1}$. What is the voltage difference developed between the ends of the wing having a span of $25 \mathrm{m}$, if the Earth’s magnetic field at the location has a magnitude of  $5\times {10}^{-4} \mathrm{T}$ and the dip angle is $30°$ ?

Figure shows a rectangular conductor $PQRS$ in which the conductor $PQ$ is free to move in a uniform magnetic field $B$ perpendicular to the plane of the paper. The field extends from $x=0$ to $x=b$ and is zero for $x>b$. Assume that only the arm $PQ$ possesses resistance $r$. When the arm $PQ$ is pulled outward from $x=0$ with constant speed $v$, the joules heating loss from $b\le x<2b$ would be:

Derive the expression for alternating EMF when the rectangular coil is rotating in a uniform magnetic field.

A rectangular frame $ABCD$ made of a uniform metal wire has a straight connection between $E$ and $F$ made of the same wire as shown in the figure. $AEFD$ is a square of side $1 \mathrm{m}$ and $EF=FC=0.5 \mathrm{m}$. The entire circuit is placed in a steadily increasing uniform magnetic field directed into the plane of the paper and normal to it. The rate of change of the magnetic field is $1 \mathrm{T} {\mathrm{s}}^{-1}$, the resistance per unit length of the wire is $1 \mathrm{\Omega } {\mathrm{m}}^{-1}$.  If the current in segments $BE$ is $\frac{x}{22} \mathrm{A}$, find $x$.

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In figure, wires $P_1{Q}_1$ and $P_2{Q}_2,$ both are moving towards right with speed $5 \mathrm{cm} {\sec }^{-1}$ resistance of each wire is $2 \mathrm{\Omega }$. Then current through resistor is $a\times {10}^{-1} \mathrm{mA}$

A metal conductor of length $1 \mathrm{m}$ rotates vertically about one of its ends at angular velocity $5 \mathrm{rad} {\mathrm{s}}^{-1}$. If the horizontal component of earth's magnetic field is  $0.2\times {10}^{-4} \mathrm{T}$, then the emf (in $\mathrm{\mu V}$) developed between the ends of the conductor is

A six-pole generator with fixed field excitation develops an emf of $100 \mathrm{V}$, when operating at $1500 \mathrm{rpm}$. At what speed (in rpm) must it rotate to develop an emf of $120 \mathrm{V}$?

A conducting rod $PQ$ of length $1 \mathrm{m}$ is moving with a uniform speed $2 {\mathrm{ms}}^{-1}$ in a uniform magnetic field of $4 \mathrm{T}$ which is directed into the paper. A capacitor of capacity $10 \mathrm{\mu F}$ is connected as shown in the figure. Then the charges on the plates of the capacitor are

A rod of length $1 \mathrm{m}$ is kept inclined at an angle of $60°$ with the uniform magnetic field of $0.5 \mathrm{T}$. If the rod is moved with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}.$ perpendicular to the field, the induced emf is

A copper rod is moved in a magnetic field. The charge developed across its ends will be proportional to _____.

A loop $\mathrm{ABCD}$ is moving with velocity $v$ towards right. The magnetic field is $2 \mathrm{T}$. Loop is connected to a resistance of $9 \mathrm{\Omega }$. If steady current of $2 \mathrm{A}$flows in the loop, then value of $v$, if loop has resistance of $4 \mathrm{\Omega }$ is (given, $\mathrm{AD}=30 \mathrm{cm}$ )

A conducting rod of length $L=1 \mathrm{m}$ is moving with a uniform speed $v=2 \mathrm{m} {\mathrm{s}}^{-1}$ on conducting rails in a magnetic field $B=5 \mathrm{T}$ as shown. On one side, the end of the rails is connected to a capacitor of capacitance $C=2 \mathrm{\mu F}.$ Then the charges on the capacitor plates are:

A flexible circular loop $20 \mathrm{cm}$ in diameter lies in a magnetic field of magnitude $B=1 \mathrm{T}$ , directed into the plane of page as shown. The loop is pulled at the points indicated by the arrows forming a loop of zero area in $0.314 \sec$. The average $\mathrm{emf}$ induced (in $\mathrm{mV}$) in the loop is.

Whenever a magnet is moved either towards or away from a conducting coil. An emf is induced then the magnitude of induced emf is independent of

Two parallel rails of a railways track, insulated from each other and with the ground, are connected to a millivoltmeter. The distance between the rails is one metre. A train is travelling with a velocity of $72 \mathrm{km}$ ${\mathrm{h}}^{-1}$ along the track. The reading of the millivotmeter (in $\mathrm{mV}$) is (Vertical component of the earth's magnetic induction is$2\times {10}^{-5}\mathrm{T})$,

A solid metal cube of edge length $2\mathrm{ }\mathrm{cm}$ is moving in a positive $y$ -direction at a constant speed of $6\mathrm{ }\mathrm{m}/\mathrm{s}$. There is a uniform magnetic field of $0.1\mathrm{ }\mathrm{T}$ in the positive $z$ -direction. The potential difference between the two faces of the cube perpendicular to the $x$ -axis, is: