Electromagnetism PYQ — Page 21

If $\vec{E}$ and $\vec{K}$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ($\omega -$ angular frequency)

The magnetic field at the center of a circular coil of radius R carrying current I is

A conducting loop of radius $\frac{10}{\sqrt{\pi }}\mathrm{cm}$ is placed perpendicular to a uniform magnetic field of $0.5T$. The magnetic field is decreased to zero in $0.5s$ at a steady rate. The induced emf in the circular loop at $0.25s$ is:

As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\pi }{10}m$ is carrying current $I=3A$. The magnitude of the magnetic field. at the center $O$ of the arc is: (The permeability of the vacuum $=4\pi \times {10}^{-7}{\mathrm{NA}}^{-2}$ ) 

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius ${r}_{A}=10\mathrm{cm}\text{and}{r}_{B}=20\mathrm{cm}$ respectively are equal if: (Where ${N}_{A},{I}_{A}\text{and}{N}_{B},{I}_{B}$ are number of turn and current of $A\text{and}B$ respectively)

A circular loop of radius $R$ is carrying current $iA$. The ratio of magnetic field at the centre of circular loop and at a distance $R$ from the center of the loop on its axis is :

In a cuboid of dimension $2L\times 2L\times L$ , a charge $q$ is placed at the centre of the surface $S$ having area of $4{L}^{2}$ . The flux through the opposite surface to $S$ is given by

A conducting circular loop is placed in a uniform magnetic field of $0.4T$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $1\mathrm{mm}{s}^{-1}$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $2\mathrm{cm}$ will be _______ $\mu V$.

A square shaped coil of area $70{\mathrm{cm}}^{2}$ having $600$ turns rotates in a magnetic field of $0.4\mathrm{Wb}{m}^{–2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes $500$ revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60^{\circ}$ with the field, will be ______ $V$. (Take $\pi =\frac{22}{7}$)

The equivalent resistance between $A\text{and}B$ is _______. .

A series LCR circuit is connected to an ac source of $220V,50\mathrm{Hz}$. The circuit contain a resistance $R=100\Omega$ and an inductor of inductive reactance ${X}_{L}=79.6\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ $\mu F$.

In a series $LR$ circuit with ${X}_{L}=R$, power factor is ${P}_{1}$. If a capacitor of capacitance $C$ with ${X}_{C}={X}_{L}$ is added to the circuit the power factor becomes ${P}_{2}$. The ratio of ${P}_{1}$ to ${P}_{2}$ will be :

Match List-I with List II of Electromagnetic waves with corresponding wavelength range: <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>(A)</td><td>Microwave</td><td>(I)</td><td>$400\mathrm{nm}$ to $1\mathrm{nm}$</td></tr><tr><td>(B)</td><td>Ultraviolet</td><td>(II)</td><td>$1\mathrm{nm}$ to ${10}^{–3}\mathrm{nm}$</td></tr><tr><td>(C)</td><td>$X$-Ray</td><td>(III)</td><td>$1\mathrm{mm}$ to $700\mathrm{nm}$</td></tr><tr><td>(D)</td><td>Infra-red</td><td>(IV)</td><td>$0.1m$ to $1\mathrm{mm}$</td></tr></tbody></table>Choose the correct answer from the options given below:

In an ac generator, a rectangular coil of $100$ turns each having area $14\times {10}^{–2}{m}^{2}$ is rotated at $360\mathrm{rev}{\mathrm{min}}^{-1}$ about an axis perpendicular to a uniform magnetic field of magnitude $3.0T$. The maximum value of the emf produced will be ______ $V$. [Take $\pi =\frac{22}{7}$]

The electric field in an electromagnetic wave is given as $\vec{E}=20\mathrm{sin}\omega (t-\frac{x}{c})\vec{j}N{C}^{-1}$, where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5\times {10}^{-4}{m}^{3}$ will be (Given ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

A wire of length $1m$ moving with velocity $8m{s}^{-1}$ at right angles to a magnetic field of $2T$. The magnitude of induced emf, between the ends of wire will be ___________.

A series LCR circuit consists of $R=80Ω$. ${X}_{L}=100Ω$, and ${X}_{C}=40Ω$. The input voltage is $2500\mathrm{cos}(100\pi t)V$. The amplitude of current, in the circuit, is _____ $A$.

Two parallel plate capacitors ${C}_{1}$ and ${C}_{2}$ each having capacitance of $10\mu F$ are individually charged by a $100V$ D.C. source. Capacitor ${C}_{1}$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor ${C}_{2}$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor ${C}_{1}$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be _____ $V$. (Assuming Dielectric constant $=10$)

A $20\mathrm{cm}$ long metallic rod is rotated with $210\mathrm{rpm}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field $0.2T$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is _________$\mathrm{mV}$. (Take $\pi =\frac{22}{7}$)

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B=0.8T$. When released the radius of the loop starts shrinking at a constant rate of $2\mathrm{cm}{s}^{–1}$. The induced emf in the loop at an instant when the radius of the loop is $10\mathrm{cm}$ will be ______ $\mathrm{mV}$.

If a copper wire is stretched to increase its length by $20%$. The percentage increase in resistance of the wire is _____%.

The distance between two plates of a capacitor is $d$ and its capacitance is ${C}_{1}$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes ${C}_{2}$ . The ratio $\frac{{C}_{2}}{{C}_{1}}$ is

An inductor of $0.5\mathrm{mH}$, a capacitor of $20\mu F$ and resistance of $20\Omega$ are connected in series with a $220V$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}A$. The value of $x$ is-

Ratio of thermal energy released in two resistor $R$ and $3R$ connected in parallel in an electric circuit is :