Electromagnetism PYQ — Page 14

Two insulated circular loop $A$ and $B$ radius $a$ carrying a current of $I$ in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be: 

A series LCR circuit is subjected to an ac signal of $200 \mathrm{~V}, 50 \mathrm{~Hz}$. If the voltage across the inductor $(\mathrm{L}=10 \mathrm{mH})$ is $31.4 \mathrm{~V}$, then the current in this circuit is _____ .

A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:

A 2 A current carrying straight metal wire of resistance $1 \Omega$, resistivity $2 \times 10^{-6} \Omega \mathrm{m}$, area of cross-section $10 \mathrm{~mm}^2$ and mass $500 \mathrm{~g}$ is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of $B$ is _____$\times 10^{-1} \mathrm{~T}$ (given, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ).

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $25 \mathrm{nF}$. If resistance of $200 \Omega$ and $100 \mathrm{mH}$ inductor is being used in the given circuit. The frequency of ac source is ______ $\times 10^3 \mathrm{~Hz}$. (given $\pi^2=10$ )

The electric field of an electromagnetic wave in free space is represented as $\vec{E}={E}_{0}\mathrm{cos}(\omega t-kz)\hat{i}$. The corresponding magnetic induction vector will be :

A capacitor of $10 \mu \mathrm{F}$ capacitance whose plates are separated by $10 \mathrm{~mm}$ through air and each plate has area $4 \mathrm{~cm}^2$ is now filled equally with two dielectric media of $\mathrm{K}_1=2, \mathrm{~K}_2=3$ respectively as shown in figure. If new force between the plates is $8 \mathrm{~N}$. The supply voltage is _________ $\times 10^{-4} \mathrm{~V}$.  (we modified language of question to make it correct)

To measure the internal resistance of a battery, potentiometer is used. For $\mathrm{R}=10 \Omega$, the balance point is observed at $l=500 \mathrm{~cm}$ and for $\mathrm{R}=1 \Omega$ the balance point is observed at $l=400 \mathrm{~cm}$. The internal resistance of the battery is approximately :

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0\mathrm{cm}$. The magnitude of the magnetic field at a point $P$ midway between the wires is $_____\mu T$. (Given: ${\mu }_{0}=4\pi \times {10}^{-7}Tm{A}^{-1}$) 

A square loop of side $10\mathrm{cm}$ and resistance $0.7\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of $0.20T$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $1s$ at a steady rate. Then, the magnitude of induced emf is $\sqrt{x}\times {10}^{-3}V$. The value of $x$ is _______.

A LCR circuit is at resonance for a capacitor $C$, inductance $L$ and resistance $R$. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

A parallel plate capacitor has a capacitance $C=200\mathrm{pF}$. It is connected to $230V$ ac supply with an angular frequency $300\mathrm{rad}{s}^{-1}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then time period will be given as: (Consider $k$ as Coulomb's constant)

The electric potential at the surface of an atomic nucleus $(Z=50)$ of radius $9\times {10}^{-13}\mathrm{cm}$ is $\alpha \times {10}^{6}V$. What is the value of $\alpha$? (Charge of proton $1.6\times {10}^{-19}C$)

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5\times {10}^{10}\mathrm{Hz}$ and an amplitude of $50V{m}^{–1}$. The total average energy density of the electromagnetic field of the wave is : [Use ${\epsilon }_{0}=8.85\times {10}^{–12}{C}^{2}{N}^{-1}{m}^{-2}$]

Two parallel long current carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is _____ 

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

The electrostatic force between two point charges q₁ and q₂ separated by distance r is given by Coulomb's law as:

When a potential difference $V$ is applied across a wire of resistance $R$, it dissipates energy at a rate $W.$ If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

Suppose a uniformly charged wall provides a uniform electric field of $2\times {10}^{4}N{C}^{-1}$ normally. A charged particle of mass $2g$ being suspended through a silk thread of length $20\mathrm{cm}$ and remain stayed at a distance of $10\mathrm{cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}}\mu C$ where $x=$ ________ [use $g=10m{s}^{-2}$]

A square loop of edge length $2 \mathrm{~m}$ carrying current of $2 \mathrm{~A}$ is placed with its edges parallel to the $x$ $y$ axis. A magnetic field is passing through the $x-y$ plane and expressed as $\vec{B}=B_0(1+4 x) \hat{k}$, where $B_0=5 \mathrm{~T}$. The net magnetic force experienced by the loop is _______ $\mathrm{N}$.

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have : (A) $E=0,B=0$; (B) $E=0,B\neq 0$; (C) $E\neq 0,B=0$; (D) $E\neq 0,B\neq 0$ Choose the most appropriate answer from the options given below :

The charge accumulated on the capacitor connected in the following circuit is ______\mu C. (Given $C=150\mu F)$ 

Force between two point charges ${q}_{1}$ and ${q}_{2}$ placed in vacuum at $r$ $\mathrm{cm}$ apart is $F$. Force between them when placed in a medium having dielectric $K=5$ at $\frac{r}{5}$ $\mathrm{cm}$ apart will be: