Electromagnetism PYQ — Page 12

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\left.\chi_{\mathrm{mg}}=1.2 \times 10^{-5}\right)$ is :

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $-\sigma$ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as $\mathrm{n}^{\text {th }}$ power of time. The numerical value of $n$ is ________.

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $\varepsilon_1$ and $\varepsilon_2$, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are $C_1$ and $C_2$ respectively, then $\frac{C_1}{C_2}$ is :  

A line charge of length $\frac{\text { ' } a \text { ' }}{2}$ is kept at the center of an edge $B C$ of a cube $A B C D E F G H$ having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda$ C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, $\epsilon_0$ as the free space permittivity) 

A loop ABCDA , carrying current $\mathrm{I}=12 \mathrm{~A}$, is placed in a plane, consists of two semi-circular segments of radius $R_1=6 \pi \mathrm{~m}$ and $\mathrm{R}_2=4 \pi \mathrm{~m}$. The magnitude of the resultant magnetic field at center O is $\mathrm{k} \times 10^{-7} \mathrm{~T}$. The value of k is ______ (Given $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}$) 

Two metal spheres of radius $R$ and $3 R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is.

An infinitely long wire has uniform linear charge density $\lambda=2 \mathrm{nC} / \mathrm{m}$. The net flux through a Gaussian cube of side length $\sqrt{3} \mathrm{~cm}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $\mathrm{xNm}^2 \mathrm{C}^{-1}$, where x is : [Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ SI units]

In the given electromagnetic wave $\mathrm{E}_{\mathrm{y}}=600 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{Vm}^{-1}$, intensity of the associated light beam is (in $\mathrm{W} / \mathrm{m}^2$ : (Given $\epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$$(L={l}^{2})$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}\times {10}^{-7}H$, where $x=$______.

Ques: $\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is :

The current of $5A$ flows in a square loop of sides $1m$ is placed in air. The magnetic field at the centre of the loop is $X\sqrt{2}\times {10}^{-7}T$. The value of $X$ is _________.

The horizontal component of earth's magnetic field at a place is $3.5\times {10}^{-5}T$. A very long straight conductor carrying current of $\sqrt{2}A$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________$\times {10}^{-6}N{m}^{-1}$.

Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter, they enter normally in a region of uniform magnetic field and describes circular paths of radii ${R}_{1}$ and ${R}_{2}$ respectively. The mass ratio of $X$ and $Y$ is :

An electric field is given by $(6\hat{i}+5\hat{j}+3\hat{k})N{C}^{-1}$. The electric flux through a surface area $30\hat{i}{m}^{2}$ lying in YZ-plane(in SI unit) is:

A coil of $200$ turns and area $0.20{m}^{2}$ is rotated at half a revolution per second and is placed in uniform magnetic field of $0.01T$ perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2\pi }{\beta }$ volt. The value of $\beta$ is ______.

A horizontal straight wire $5m$ long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $0.60\times {10}^{-4}\mathrm{Wb}{m}^{-2}$. The instantaneous value of emf induced in the wire when its velocity is $10m{s}^{-1}$ is _______$\times {10}^{-3}V$.

The current flowing through the $1 \Omega$ resistor is $\frac{n}{10}$ A. The value of $n$ is _________ 

Primary coil of a transformer is connected to $220VAC$. Primary and secondary turns of the transforms are $100$ and $10$ respectively. Secondary coil of transformer is connected to two series resistances as shown in figure. The output voltage $({V}_{0})$ is : 

The primary side of a transformer is connected to $230V,50\mathrm{Hz}$ supply. The turn ratio of primary to secondary winding is $10:1$. Load resistance connected to the secondary side is $46\Omega$. The power consumed in it is:

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :

An alternating voltage $V(t)=220\mathrm{sin}100\pi t$ volt is applied to a purely resistive load of $50\Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

Match List-I with List-II : $\begin{array}{|c|c|c|c|} \hline & \text { List-I } & & \text { List-II } \\ \hline & \text { EM-Wave } & & \text { Wavelength Range } \\ \hline \text { (A) } & \text { Infra-red } & \text { (I) } & < 10^{-3} \mathrm{~nm} \\ \hline \text { (B) } & \text { Ultraviolet } & \text { (II) } & 400 \mathrm{~nm} \text { to } 1 \mathrm{~nm} \\ \hline \text { (C) } & \text { X-rays } S & \text { (III) } & 1 \mathrm{~mm} \text { to } 700 \mathrm{~nm} \\ \hline \text { (D) } & \text { Gamma rays } & \text { (IV) } & 1 \mathrm{~nm} \text { to } 10^{-3} \mathrm{~nm} \\ \hline \end{array}$

A galvanometer of resistance $100 \Omega$ when connected in series with $400 \Omega$ measures a voltage of upto $10 \mathrm{~V}$. The value of resistance required to convert the galvanometer into ammeter to read upto $10 \mathrm{~A}$ is $x \times 10^{-2} \Omega$. The value of $x$ is :

By what percentage will the illumination of the lamp decrease if the current drops by $20%$?