Motional Electromotive Force

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 conducting $rodAC$ of length $4l$ and mass $m$ is rotating about point $O$ with angular momentum $J.$ A uniform magnetic field $B$ is directed into the paper. Given, $AO=l$ and $OC=3l.$ Then, $V_A-V_C$ is $\lambda$ times $\frac{BJ}{14M}$. What is the value of $\lambda$?

A rod of length $5 \mathrm{cm}$ is fixed at one end and it is rotating with an angular speed of $5 \mathrm{rad}/\mathrm{s}$. There is a magnetic field of $2 \mathrm{T}$ along the axis of rotation of the field. Find the EMF induced in the rod in millivolts.

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, $\mathrm{AD}=30 \mathrm{cm}$ )

The total charge induced in a conducting loop, when it is moved in magnetic field depends on

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 semicircular insulated conductor of radius $0.5$ $\mathrm{m}$ (lying in $X-Z$ plane) is rotated at uniform angular speed of $4$$\mathrm{rad}{\mathrm{s}}^{-1}$ about an axis passing through one of the ends of the conductor (say $A$) in the presence of an external uniform magnetic field $B_0$. Both the axis of rotation and the magnetic field are normal to the plane of the semicircle. If the induced voltage between the ends of the conductor is $10$ $\mathrm{mV}$. What is the strength of magnetic field in $\mathrm{mT}$ ?

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 copper rod of length $l$ is rotated about one end, perpendicular to the magnetic field $B$, with constant angular velocity $\mathrm{\omega }$. The induced emf between the two ends of the rod is,

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:

The total charge, induced in a conducting loop, when it is moved in a magnetic field depends on

A cycle wheel with $10$ spokes each of length $0.5 \mathrm{m}$ long is rotated at a speed of $18 \mathrm{km}/\mathrm{hr}$ in a plane normal to the earth's magnetic induction of $3.6\times {10}^{-5} \mathrm{T}$. Calculate the e.m.f. induced between the (i) axle and the rim of the cycle wheel. (ii) ends of single spoke and ten spokes.

A $20 \mathrm{cm}$ conducting long wire is placed perpendicular to $5\times {10}^{-4} \mathrm{Wb}/{\mathrm{m}}^2$ magnetic field. Wire is moving perpendicular to its length and magnetic field. If wire moves $1 \mathrm{m}$ in $4 \sec$, then find induced emf between its ends. 

A conductor of length $–3 \hat{\mathrm{k}} \mathrm{m}$ is moving with velocity $\left(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\right) \mathrm{m}/\mathrm{s}$ in $\left(\mathrm{i}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}\right) \mathrm{T}$ magnetic field. Find out potential difference across the ends of conductor. 

A rectangular loop is moving perpendicular to a non-uniform magnetic field with constant velocity. Find out the expression for induced emf and current and also prove that the law of conservation of energy holds good here.

A conducting wire is moving towards right (with velocity $v$) in magnetic field $B$. If direction of induced current is as shown in figure then the direction of magnetic field is-

A copper wire coil $\mathrm{C}$ and a wire are place in the plane of paper as shown in figure. If current in wire increases from $1 \mathrm{A}$ to $2 \mathrm{A}$ along the direction show in figure, then what is the direction of induced current in coil-