Electromagnetism PYQ — Page 19

An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm{Cm}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

A square loop of side $15 \mathrm{~cm}$ being moved towards right at a constant speed of 2 $\mathrm{cm} / \mathrm{s}$ as shown in figure. The front edge enters the $50 \mathrm{~cm}$ wide magnetic field at $t=$ 0 . The value of induced emf in the loop at $t=10 \mathrm{~s}$ will be : 

A plane electromagnetic wave propagating in $x$-direction is described by ${E}_{y}=(200V{m}^{-1})\mathrm{sin}[1.5\times {10}^{7}t-0.05x];$The intensity of the wave is : (Use ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of ' $\mathrm{m}$ ' number of turns. It carries a current of $5 \mathrm{~A}$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \mathrm{~T}$ then the value of $m$ is _____.

A capacitor of capacitance $C$ and potential $V$ has energy $E.$ It is connected to another capacitor of capacitance $2C$ and potential $2V$. Then the loss of energy is $\frac{x}{3}E$, where $x$ is _______.

A galvanometer $(G)$ of $2\Omega$ resistance is connected in the given circuit. The ratio of charge stored in ${C}_{1}$ and ${C}_{2}$ is: 

A circular coil having 200 turns, $2.5 \times 10^{-4} \mathrm{~m}^2$ area and carrying $100 \mu \mathrm{A}$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^{\circ}$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is ______ $\mu \mathrm{J}$.

Five charges $+q,+5 q,-2 q,+3 q$ and $-4 q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is : 

A coil of negligible resistance is connected in series with $90 \Omega$ resistor across $120 \mathrm{~V}, 60 \mathrm{~Hz}$ supply. A voltmeter reads $36 \mathrm{~V}$ across resistance. Inductance of the coil is :

A alternating current at any instant is given by $i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$ A. The $r m s$ value of the current is ________ A.

In the given figure $\mathrm{R}_1=10 \Omega, \mathrm{R}_2=8 \Omega, \mathrm{R}_3=4 \Omega$ and $\mathrm{R}_4=8 \Omega$. Battery is ideal with emf $12 \mathrm{~V}$. Equivalent resistant of the circuit and current supplied by battery are respectively : 

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20\mathrm{cm}$ from its center is $1.5\times {10}^{-5}Tm$. The magnetic moment of the dipole is _______ $A{m}^{2}$. (Given : $\frac{{\mu }_{0}}{4\pi }={10}^{-7}Tm{A}^{-1}$)

A uniform magnetic field of $2\times {10}^{-3}T$ acts along positive Y-direction. A rectangular loop of sides $20\mathrm{cm}$ and $10\mathrm{cm}$ with current of $5A$ is in Y-Z plane. The current is in anticlockwise sense with reference to negative X axis. Magnitude and direction of the torque is :

A thin metallic wire having cross sectional area of ${10}^{-4}{m}^{2}$ is used to make a ring of radius $30\mathrm{cm}$. A positive charge of $2\pi C$ is uniformly distributed over the ring, while another positive charge of $30\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is $_______N$; provided that the ring does not get deformed (neglect the influence of gravity). (Given, $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}$ SI units)

An AC voltage $V=20\mathrm{sin}200\pi t$ is applied to a series LCR circuit which drives a current $I=10\mathrm{sin}(200\pi t+\frac{\pi }{3})$. The average power dissipated is:

The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is : 

When a coil is connected across a $20 \mathrm{~V}$ dc supply, it draws a current of $5 \mathrm{~A}$. When it is connected across $20 \mathrm{~V}, 50 \mathrm{~Hz}$ ac supply, it draws a current of $4 \mathrm{~A}$. The self inductance of the coil is ______ $\mathrm{mH}$. $($ Take $\pi=3$ )

In a metre-bridge when a resistance in the left gap is $2\Omega$ and unknown resistance in the right gap, the balance length is found to be $40\mathrm{cm}.$ On shunting the unknown resistance with $2\Omega ,$ the balance length changes by:

If frequency of electromagnetic wave is $60\mathrm{MHz}$ and it travels in air along $z$ direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave $(\mathrm{in}m)$ is :

A series $LR$ circuit connected with an ac source $E=(25\mathrm{sin}1000t)V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E=(20\mathrm{sin}2000t)V$, the new power factor of the circuit will be :

An electric field $\vec{E}=(2 x \hat{i}) N C^{-1}$ exists in space. A cube of side $2 \mathrm{~m}$ is placed in the space as per figure given below. The electric flux through the cube is ______ $\mathrm{Nm}^2 / \mathrm{C}$. 

If the net electric field at point $\mathrm{P}$ along $\mathrm{Y}$ axis is zero, then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$, where $x=$ _____. 

A parallel plate capacitor of capacitance $12.5 \mathrm{pF}$ is charged by a battery connected between its plates to potential difference of $12.0 \mathrm{~V}$. The battery is now disconnected and a dielectric slab $\left(\epsilon_{\mathrm{r}}=6\right)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _____ $10^{-12} \mathrm{~J}$.

Two coils have mutual inductance $0.002H$. The current changes in the first coil according to the relation $i={i}_{0}sin\omega t$, where ${i}_{0}=5A$ and $\omega =50\pi$ $\mathrm{rad}{s}^{-1}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi }{\alpha }V$. The value of $\alpha$ is