Electromagnetism PYQ — Page 22

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 _____. 

For a uniformly charged thin spherical shell, the electric potential $(V)$ radially away from the centre $(O)$ of shell can be graphically represented as 

The magnetic intensity at the centre of a long current carrying solenoid is found to be $1.6\times {10}^{3}A{m}^{-1}$. If the number of turns is $8$ per $\mathrm{cm}$, then the current flowing through the solenoid is $______A.$

An LCR series circuit of capacitance $62.5\mathrm{nF}$ and resistance of $50\Omega$, is connected to an A.C. source of frequency $2.0\mathrm{kHz}$. For maximum value of amplitude of current in circuit, the value of inductance is ____$\mathrm{mH}$.$(\text{Take}{\pi }^{2}=10)$

A parallel plate capacitor has plate area $40{\mathrm{cm}}^{2}$ and plates separation $2\mathrm{mm}$. The space between the plates is filled with a dielectric medium of a thickness $1\mathrm{mm}$ and dielectric constant $5$. The capacitance of the system is:

Three identical resistors with resistance $R=12\Omega$ and two identical inductors with sell inductance $L=5\mathrm{mH}$ are connected to an ideal battery with emf of $12V$ as shown in figure. The current through the battery long after the switch has been closed will be________$A$. 

Figure shows a part of an electric circuit. The potentials at points $a,b$ and $c$ are $30V,12V$ and $2V$ respectively. The current through the $20\Omega$ resistor will be, 

The resistance of a wire is $5\Omega$. Its new resistance in ohm, if stretched to $5$ times of its original length will be :

A series LCR circuit is connected to an AC source of $220V$, $50\mathrm{Hz}$. The circuit contains a resistance $R=80\Omega$, an inductor of inductive reactance ${X}_{L}=70\Omega$, and a capacitor of capacitive reactance ${X}_{C}=130\Omega$. The power factor of circuit is $\frac{x}{10}$. The value of $x$ is:

A cubical volume is bounded by the surfaces $x=0,x=a,y=0,y=a,z=0,z=a$. The electric field in the region is given by $\vec{E}={E}_{0}x\hat{i}$. Where ${E}_{0}=4\times {10}^{4}{\mathrm{NC}}^{-1}{m}^{-1}$. If $a=2\mathrm{cm}$, the charge contained in the cubical volume is $Q\times {10}^{–14}C$. The value of $Q$ is ______. (Take ${\epsilon }_{0}=9\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

An alternating voltage source $V=260\mathrm{sin}(628t)$ is connected across a pure inductor of $5\mathrm{mH}$. Inductive reactance in the circuit is:

Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as ${E}_{0}=\sqrt{\frac{{\mu }_{0}}{{\epsilon }_{0}}}{B}_{0}$. In the light of the above statements, choose the correct answer from the options given below:

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by ${E}_{x}={E}_{0}\mathrm{sin}(kz-\omega t)$ ${B}_{y}={B}_{0}\mathrm{sin}(kz-\omega t)$ Then the correct relation between ${E}_{0}$ and ${B}_{0}$ is given by

Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge ${q}_{0}$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is ______.

Given below are two statements: Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an $AC$ source, when resonance occurs. Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, 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 : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

For designing a voltmeter of range $50V$ and an ammeter of range $10\mathrm{mA}$ using a galvanometer which has a coil of resistance $54Ω$ showing a full scale deflection for $1\mathrm{mA}$ as in figure.  (A) for voltmeter $R\approx 50kΩ$ (B) for ammeter $r\approx 0.2Ω$ (C) for ammeter $r\approx 6Ω$ (D) for voltmeter $R\approx 5kΩ$ (E) for voltmeter $R\approx 500Ω$ Choose the correct answer from the options given below:

A rectangular parallelopiped is measured as $1\mathrm{cm}\times 1\mathrm{cm}\times 100\mathrm{cm}$. If its specific resistance is $3\times {10}^{-7}\Omega m$, then the resistance between its two opposite rectangular faces will be _____$\times {10}^{-7}\Omega$. 

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 $\mathrm{mV}$. 

The waves emitted when a metal target is bombarded with high energy electrons are

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.

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 $1\times 2\times 3{m}^{3}$)