Electromagnetism PYQ — Page 24

A metallic cube of side $15\mathrm{cm}$ moving along $y$-axis at a uniform velocity of $2m{s}^{-1}$. In a region of uniform magnetic field of magnitude $0.5T$ directed along $z$- axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be $\mathrm{mV}$. 

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-

The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of coil on its axis is $\sqrt{x}:1$. The value of $x$ is _____.

As shown in the figure, a configuration of two equal point charges $({q}_{0}=+2\mu C)$ is placed on an inclined plane. Mass of each point charge is $20g$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $h=x\times {10}^{-3}m$. The value of$x$ is $(\text{ Take }\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2},g=10m{s}^{-2})$ 

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

An inductor of inductance $2\mu H$ is connected in series with a resistance, a variable capacitor and an AC source of frequency $7\mathrm{kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}F$, where the value of $x$ is ______. (Take $\pi =\frac{22}{7}$)

Given below are two statements: Statement I : When the frequency of an AC source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement II : In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below.

The equivalent resistance between $A$ and $B$ as shown in figure is: 

As shown in figure, a cuboid lies in a region with electric field $E=2{x}^{2}\hat{i}-4y\hat{j}+6\hat{k}N{C}^{-1}$. The magnitude of charge within the cuboid is $n{\epsilon }_{0}C$. The value of $n$ is ______ (if dimension of cuboid is $1\times 2\times 3{m}^{3}$) 

In the given circuit.${C}_{1}=2\mu F,{C}_{2}=0.2\mu F,{C}_{3}=2\mu F,{C}_{4}=4\mu F,{C}_{5}=$ $2\mu F,{C}_{6}=2\mu F$. The charge stored on capacitor ${C}_{4}$ is ______ $\mu C$. 

The magnetic field B crossing normally a square metallic plate of area $4{m}^{2}$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $t=2s$ to $t=4s$, is _____ $mV$. 

Two concentric circular coils with radii $1\mathrm{cm}$ and $1000\mathrm{cm}$ and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____ $\times {10}^{–8}H$. (Take, ${\pi }^{2}=10$)

A solenoid of $1200$ turns is wound uniformly in a single layer on a glass tube $2m$ long and $0.2m$ in diameter. The magnetic intensity at the center of the solenoid when a current of $2A$ flows through it is:

Match List I and List II <table class="pyq-table"><tbody><tr><td>A</td><td>Gauss’s Law in Electrostatics</td><td>I</td><td>$\oint \vec{E}\cdot \vec{dl}=-\frac{d{\phi }_{B}}{dt}$</td></tr><tr><td>B</td><td>Faraday's Law</td><td>II</td><td>$\oint \vec{B}\cdot d\vec{A}=0$</td></tr><tr><td>C</td><td>Gauss’s Law in Magnetism</td><td>III</td><td>$\oint \vec{B}\cdot d\vec{l}={\mu }_{0}{i}_{c}+{\mu }_{0}{\in }_{0}\frac{d{\phi }_{E}}{dt}$</td></tr><tr><td>D</td><td>Ampere-Maxwell Law</td><td>IV</td><td>$\oint \vec{E}\cdot d\vec{s}=\frac{q}{{\in }_{0}}$</td></tr></tbody></table>Choose the correct answer from the options given below :

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Assertion A : Electromagnets are made of soft iron. Reason R : Soft iron has high permeability and low retentivity. In the light of above statements, choose the most appropriate answer from the options given below.

An oscillating $\mathrm{LC}$circuit consists of a $75\mathrm{mH}$ inductor and a $1.2\mu F$ capacitor. If the maximum charge to the capacitor is $2.7\mu C$. The maximum current in the circuit will be $_______\mathrm{mA}$.

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

Two identical cells each of emf $1.5V$ are connected in series across a $10\Omega$ resistance. An ideal voltmeter connected across $10\Omega$ resistance reads $1.5V$. The internal resistance of each cell is _____ $\Omega$.

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R,$with distance $r$ from the centre $O$ is represented by: 

If two charges ${q}_{1}$and ${q}_{2}$ are separated with distance $d$ and placed in a medium of dielectric constant $k$. What will be the equivalent distance between charges in air for the same electrostatic force?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below.

A massless square loop, of wire of resistance $10\Omega$, supporting a mass of $1g$, hangs vertically with one of its sides in a uniform magnetic field of ${10}^{3}G$, directed outwards in the shaded region. A dc voltage $V$ is applied to the loop. For what value of $V$, the magnetic force will exactly balance the weight of the supporting mass of $1g$? (If sides of the loop $=10\mathrm{cm},g=10m{s}^{-2}$) .

In the given figure, an inductor and resistor are connected in series with a battery of $\mathrm{emf}$ $E$ volt. $\frac{{E}^{a}}{2b}J{s}^{-1}$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ will be _____. 

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: