Academic Experts Solutions for Chapter: Electromagnetic Induction, Exercise 9: Motion EMF Due to Motion of Conductor in Magnetic Field

A conducting rod $AB$ of length $l=1 \mathrm{m}$, is moving with a velocity $v=4 \mathrm{m} {\mathrm{s}}^{-1}$, making an angle ${30}^{\circ }$ with its length. A uniform magnetic field, $B=2 \mathrm{T}$, exists in a direction perpendicular to the plane of motion. The potential difference between the end of the rod is 

A wire $X-Y$, of length$l$, mass $m$ and resistance $R$, slides without friction, down an inclined parallel rails. The resistance of the rails is negligible and rails make an angle $\mathrm{\theta }$ with the horizontal. If uniform and vertically downward magnetic field exists throughout the region, then the steady state terminal velocity acquired by the wire, will be

One conducting U-tube can slide inside another, as shown in the figure, maintaining electrical contact between the tubes. The magnetic field $B$ is perpendicular to the plane of the figure. If each tube moves towards the other, at a constant speed $v$, then the emf $\epsilon$ induced in the circuit, in terms of $B$, $l$ and $v$, where $l$ is the width of each tube, will be 

A boat is moving due east, in a region where the Earth's magnetic field is $5.0\times {10}^{-5} \mathrm{T}$, due north and horizontal. The boat carries a vertical wire, which is $2 \mathrm{m}$ long. If the speed of the boat is $1.50 \mathrm{m} {\mathrm{s}}^{-1}$, the magnitude of the induced emf in the wire is

A conducting rod $PQ$ of length $5 \mathrm{m}$, making an angle of $53°$ with the horizontal, as shown in the figure, is kept in a magnetic field of $\left(3\hat{\mathrm{j}}+4\hat{\mathrm{k}}\right) \mathrm{T}$ and moving with velocity $2\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{-1}$ without any rotation. What is the emf induced in the rod?

A solid conducting sphere of radius $R$ is moving with a velocity $\overrightarrow{v}$, in a uniform magnetic field of strength $\overrightarrow{B}$, which is perpendicular to $\overrightarrow{v}$. The maximum emf induced between any two points of the sphere is

A horizontal straight wire $20 \mathrm{m}$ long extending from east to west is falling with a speed of $5.0 \mathrm{m} {\mathrm{s}}^{-1}$, at right angles to the horizontal component of the Earth's magnetic field which has a magnitude of $0.30\times {10}^{-4} \mathrm{wb} {\mathrm{m}}^{-2}$. The instantaneous value of the emf induced in the wire will be 

A conducting rod $PQ$ of length $L=1.0 \mathrm{m}$ is moving with a uniform speed $v=20 \mathrm{m} {\mathrm{s}}^{-1}$, in a uniform magnetic field $B=4.0 \mathrm{T}$, directed into the paper. A capacitor of capacity $C=10 \mathrm{\mu F}$ is connected, as shown in the figure. Then,