B M Sharma Solutions for Chapter: Electromagnetic Induction, Exercise 3: DPP

A metallic square loop $ABCD$ is moving in its own plane, with velocity $v$, in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced:

The figure shows four wire loops with edge lengths which are either $L$ or $2L$. All four loops will move through a region of uniform magnetic field $\overrightarrow{B}$ (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the emf induced as they move through the field.

At a place, the value of horizontal component of the earth's magnetic field $H$ is $3\times {10}^{-5}$ $\mathrm{weber} {\mathrm{m}}^{-2}$. A metallic rod $AB$ of length $2 \mathrm{m}$ placed in east-west direction, having the end A towards east, falls vertically downward with a constant velocity of $50 \mathrm{m} {\mathrm{s}}^{-1}$. Which end of the rod becomes positively charged and what is the value of induced potential difference between the two ends?

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity. If the wire $AB$ is replaced by semi-circular wire, the magnitude of the induced current will:

A straight wire of length $L$ is bent into a semicircle. It moves in a uniform magnetic field with speed $v$ and diameter perpendicular to the field. The induced emf between the ends of the wire is,

A conductor $ABOCD$ moves along its bisector with a velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$ through a perpendicular magnetic field of $1 \mathrm{Wb} {\mathrm{m}}^{-2}$, as shown in the figure. If all the four sides are of $1 \mathrm{m}$ length each, then the induced emf between points $A$ and $D$ is,

As shown in the figure, a metal rod makes contact and completes the circuit. The circuit is perpendicular to the magnetic field, $B=0.15$ $\mathrm{T}$. If the resistance is $3 \mathrm{\Omega }$, the force needed to move the rod, as indicated with a constant speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$ is,

Figure $\left(\mathrm{i}\right)$ shows a conducting loop being pulled out of a magnetic field with a speed $v$. Which of the four plots, shown in figure $\left(\mathrm{ii}\right)$, may represent the power delivered by a pulling agent as a function of the speed $v$?