Electromagnetism PYQ — Page 31

In the figure, a very large plane sheet of positive charge is shown. ${P}_{1}$ and ${P}_{2}$ are two points at distance $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields ${E}_{1}$ and ${E}_{2}$ at ${P}_{1}$ and ${P}_{2}$ respectively are 

What will be the most suitable combination of three resistors $A=2\Omega ,B=4\Omega ,C=6\Omega$ so that $(\frac{22}{3})\Omega$ is equivalent resistance of combination?

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi =(5{t}^{3}+4{t}^{2}+2t-5)$ Weber. If the resistance of the coil is $5\mathrm{ohm}$, then the induced current through the coil at $t=2s$ will be,

The electric current in a circular coil of $2$ turns produces a magnetic induction ${B}_{1}$ at its centre. The coil is unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction ${B}_{2}$ at its centre. The ratio of $\frac{{B}_{2}}{{B}_{1}}$ is:

Two long parallel conductors ${S}_{1}$ and ${S}_{2}$ are separated by a distance $10\mathrm{cm}$ and carrying currents of $4A$ and $2A$ respectively. The conductors are placed along $x$-axis in $X-Y$ plane. There is a point $P$ located between the conductors (as shown in figure). A charge particle of $3\pi$ coulomb is passing through the point $P$ with velocity $\vec{v}=(2\hat{i}+3\hat{j})m{s}^{-1}$; where $\hat{i}$ & $\hat{j}$ represents unit vector along $x$ & $y$axis respectively. The force acting on the charge particle is $4\pi \times {10}^{-5}(-x\hat{i}+2\hat{j})N$. The value of $x$ is 

In the given circuit, the magnitude of ${V}_{L}$ and ${V}_{C}$ are twice that of ${V}_{R}$. Given that $f=50\mathrm{Hz}$, the inductance of the coil is $\frac{1}{K\pi }\mathrm{mH}$. The value of $K$ is _____ . 

A parallel plate capacitor with plate area $A$ and plate separation $d=2m$ has a capacitance of $4\mu F$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $K=3$ (as shown in figure) will be 

A source of potential difference $V$ is connected to the combination of two identical capacitors as shown in the figure. When key $K$ is closed, the total energy stored across the combination is ${E}_{1}$. Now key $K$ is opened and dielectric of dielectric constant $5$ is introduced between the plates of the capacitors. The total energy stored across the combination is now ${E}_{2}$. The ratio $\frac{{E}_{1}}{{E}_{2}}$ will be 

The equation of current in a purely inductive circuit is $5\mathrm{sin}(49\pi t-30^{\circ})$. If the inductance is $30\mathrm{mH}$ then the equation for the voltage across the inductor, will be

A slab of dielectric constant $K$ has the same crosssectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}d$, where $d$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given ${C}_{0}=$ capacitance of capacitor with air as medium between plates.)

Two electric dipoles of dipole moments $1.2\times {10}^{-30}\mathrm{cm}$ and $2.4\times {10}^{-30}\mathrm{cm}$ are placed in two difference uniform electric fields of strengths $5\times {10}^{4}N{C}^{-1}$ and $15\times {10}^{4}N{C}^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is _____ .

The displacement current of $4.425\mu A$ is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of ${10}^{6}V{s}^{-1}$. The area of each plate of the capacitor is $40{\mathrm{cm}}^{2}$. The distance between each plate of the capacitor is $x\times {10}^{-3}m$. The value of $x$ is , (Permittivity of free space, ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$) _______

Two cells of the same EMF $E$ but different internal resistances ${r}_{1}$ and ${r}_{2}$ are connected in series with an external resistance $R$ as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance $R$ must then be: 

An electric bulb is rated as $200W$. What will be the peak magnetic field at $4m$ distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $3.5%$ efficiency.

A wire $X$ of length $50\mathrm{cm}$ carrying a current of $2A$ is placed parallel to a long wire $Y$ of length $5m$. The wire $Y$ carries a current of $3A$. The distance between two wires is $5\mathrm{cm}$ and currents flow in the same direction. The force acting on the wire $Y$ is : 

Given below are two statements : Statement-I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement-II: In ac circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below

A triangular shaped wire carrying $10A$ current is placed in a uniform magnetic field of $0.5T$, as shown in figure. The magnetic force on segment $CD$ is (Given $BC=CD=BD=5\mathrm{cm}$). 

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. A. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. B. The energy in electromagnetic wave is divided equally between electric and magnetic fields. C. Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. D. The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. E. The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate 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) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle $(q)$ revolves around the cylinder in a circular path. The kinetic energy of the particle is :

In the given figure of meter bridge experiment, the balancing length $AC$ corresponding to null deflection of the galvanometer is $40\mathrm{cm}$. The balancing length, if the radius of the wire $AB$ is doubled, will be _____ $\mathrm{cm}$. 

A $1m$ long copper wire carries a current of $1A$. If the cross section of the wire is $2.0{\mathrm{mm}}^{2}$ and the resistivity of copper is $1.7\times {10}^{-8}\Omega m$. The force experienced by moving electron in the wire is _____$\times {10}^{-23}N$ (Charge of electron$=1.6\times {10}^{-19}C$ )

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be (Assume the coil to be short circuited.)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils. Reason R: Constantan and manganin have very small value of temperature coefficient of resistance. In the light of the above statements, choose the correct answer from the options given below.