Electromagnetism PYQ — Page 44

Match List - I with List - II.<table class="pyq-table"><tbody><tr><td colspan="2" rowspan="1">List-I</td><td colspan="2" rowspan="1">List-II</td></tr><tr><td>(a)</td><td>Source of microwave frequency</td><td>(i)</td><td>Radioactive decay of nucleus</td></tr><tr><td>(b)</td><td>Source of infrared frequency</td><td>(ii)</td><td>Magnetron</td></tr><tr><td>(c)</td><td>Source of Gamma Rays</td><td>(iii)</td><td>Inner shell electrons</td></tr><tr><td>(d)</td><td>Source of $X$-rays</td><td>(iv)</td><td>Vibration of atoms and molecules</td></tr><tr><td></td><td></td><td>(v)</td><td>LASER</td></tr><tr><td></td><td></td><td>(vi)</td><td>RC circuit</td></tr></tbody></table>Choose the correct answer from the options given below:

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given the area of the plate $=A$ ) 

 A capacitor of capacitance $C=1\mu F$ is suddenly connected to a battery of $100V$ through a resistance $R=100\Omega .$ The time taken for the capacitor to be charged to get $50V$ is: (Take $\mathrm{ln}2=0.69$)

A capacitor is connected to a $20V$ battery through a resistance of $10\Omega .$ It is found that the potential difference across the capacitor rises to $2V$ in $1\mu s.$ The capacitance of the capacitor is $________\mu F.$ Given In $(\frac{10}{9})=0.105$

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of $15\Omega$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of $10V$ is maintained across AC. 

Red light differs from blue light as they have :

Choose the incorrect statement: (a) The electric lines of force entering into a Gaussian surface provide negative flux. (b) A charge $q$ is placed at the centre of a cube. The flux through all the faces will be the same. (c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. (d) When an electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given below:

A resistor develops $500J$ of thermal energy in $20s$ when a current of $1.5A$ is passed through it. If the current is increased from $1.5A$ to $3A$, what will be the energy developed in $20s$.

An electromagnetic wave of frequency $5\mathrm{GHz}$, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are $2.$ Its velocity in this medium is _______$\times {10}^{7}m{s}^{-1}$.

Two identical conducting spheres with negligible volume have $2.1\mathrm{nC}$ and $-0.1\mathrm{nC}$ charges, respectively. They are brought into contact and then separated by a distance of $0.5m$. The electrostatic force acting between the spheres is ___$\times {10}^{-9}N$. [Given : $4\pi {\epsilon }_{0}=\frac{1}{9\times {10}^{9}}$ SI unit]

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

An inductor of $10\mathrm{mH}$ is connected to a $20V$ battery through a resistor of $10k\Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after $1\mu s$ is $\frac{x}{100}\mathrm{mA}$. Then $x$ is equal to ______ . (Take ${e}^{-1}=0.37$)

An AC circuit has an inductor and a resistor of resistance $R$ in series, such that ${X}_{L}=3R$. Now, a capacitor is added in series such that ${X}_{C}=2R$. the ratio of the new power factor with the old power factor of the circuit is $\sqrt{5}:x$. The value of $x$ is

The electric field in an electromagnetic wave is given by $E=(50N{C}^{-1})\mathrm{sin}\omega (t-\frac{x}{c})$ The energy contained in a cylinder of volume $V$ is $5.5\times {10}^{-12}J.$ The value of $V$ is _______ ${\mathrm{cm}}^{3}.$ (given ${\epsilon }_{0}=8.8\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

An electromagnetic wave of frequency $3\mathrm{GHz}$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be _________ $\times {10}^{-2}\mathrm{cm}.$

The electric field in a plane electromagnetic wave is given by, $E=50\mathrm{sin}(500x-10\times {10}^{10}t)V{m}^{-1}$. The velocity of an electromagnetic wave in this medium is: (Given $c=$ the speed of light in vacuum).

A particle of charge $q$ and mass $m$ is moving with a velocity $-v\hat{i}(v\neq 0)$ towards a large screen placed in the $Y-Z$ plane at distance d. If there is magnetic field $\vec{B}={B}_{0}\hat{k},$ the minimum value of $v$ for which the particle will not hit the screen is :

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side $10\mathrm{cm},50$ turns and carrying current$I$ (Ampere) in units of $\frac{{\mu }_{0}I}{\pi }$ is :

A wire of resistance R is bent to form a complete circle. The resistance between two diametrically opposite points is:

Consider two charged metallic spheres ${S}_{1}$ and ${S}_{2}$ of radii ${R}_{1}$ and ${R}_{2},$ respectively. The electric fields ${E}_{1}$ (on ${S}_{1}$ ) and ${E}_{2}$ (on ${S}_{2}$ ) on their surfaces are such that $\frac{{E}_{1}}{{E}_{2}}=\frac{{R}_{1}}{{R}_{2}}.$ Then the ratio ${V}_{1}$ (on ${S}_{1}$ )$/$${V}_{2}$ (on ${S}_{2}$ ) of the electrostatic potentials on each sphere is:

Proton with kinetic energy of $1MeV$ moves from south to north. It gets an acceleration of ${10}^{12}m/{s}^{2}$ by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is $1.6\times {10}^{-27}kg$ )

A part of a complete circuit is shown in the figure. At some instant, the value of current I is $1A$ and it is decreasing at a rate of ${10}^{2}{\mathrm{As}}^{-1}$. The value of the potential difference ${V}_{p}-{V}_{Q},$ (in volts) at that instant is- 

The magnetic field of a plane electromagnetic wave is $\vec{B}=3\times {10}^{-8}\mathrm{sin}[200\pi (y+ct)]\hat{i}T$ . Where, $c=3\times {10}^{8}m{s}^{-1}$ is the speed of light the corresponding electric filed is :