Electromagnetism PYQ — Page 45

If the magnetic field in a plane electromagnetic wave is given by $\vec{B}=3\times {10}^{-8}\mathrm{sin}⁡(1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{j}T,$ then what will be expression for electric field ?

In a series $\mathrm{LR}$ circuit, power of $400W$ is dissipated from a source of $250V,50\mathrm{Hz}$. The power factor of the circuit is $0.8$. In order to bring the power factor to unity, a capacitor of value $C$ is added in series to the $L$ and $R$. Taking the value of $C$ as $(\frac{n}{3\pi })\mu F$, then value of $n$ is

An electron is constrained to move along the $y$-axis with a speed of $0.1c$ (c is the speed of light) in the presence of electromagnetic wave, whose electric field is $\vec{E}=30\hat{j}\mathrm{sin}(1.5\times {10}^{7}t-5\times {10}^{-2}x)V{m}^{-1}.$ where $t$ in in seconds and $x$ is im meters.The maximum magnetic force experienced by the electron will be: (given $c=3\times {10}^{8}m{s}^{-1}$ and electron charge $=1.6\times {10}^{-19}\mathrm{Coloumbs}$

Magnetic materials used for making permanent magnets $(P)$ and magnets in a transformer $(T)$ have different properties of the following, which property best matches for the type of magnet required?

Effective capacitance of parallel combination of two capacitors ${C}_{1}$ and ${C}_{2}$ is $10\mu F.$ When these capacitors are individually connected to a voltage source of $1V,$ the energy stored in the capacitor ${C}_{2}$ is $4$ times that of ${C}_{1}.$ If these capacitors are connected in series, their effective capacitance will be:

An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns/length and carries a current $I.$ The electron gun shoots an electron along the radius of the solenoid with speed $v.$ If the electron does not hit the surface of the solenoid, maximum possible value of $v$ is (all symbols have their standard meaning): 

An electric dipole of moment $\vec{\text{p}}=(-\hat{i}-3\hat{j}+2\hat{k})\times {10}^{-29}\text{C m}$ at the origin $(0,0,0)$ . The electric field due to this dipole at $\vec{\text{r}}=+\hat{i}+3\hat{j}+5\hat{k}$ (note that $\vec{r}\cdot \vec{p}=0$ ) is parallel to:

Four resistance $40\Omega ,60\Omega ,90\Omega$ $110\Omega$ and make the arms of a quadrilateral $ABCD$. Across $AC$ is a battery of emf $40V$ and internal resistance negligible. The potential difference across $BD$ in $V$ is __________ 

Radiation, with wavelength $6561Å$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3\times {10}^{-4}T$ . If the radius of the largest circular path followed by the electrons is $10mm$ , the work function of the metal is close to:

A long solenoid of radius $R$ carries a time $(t)$ dependent current $I(t)={I}_{0}t(1-t)$ . A ring of radius $2R$ is placed coaxially near its middle. During the time interval $0\leq t\leq 1,$ the induced current $({I}_{R})$ and the induced $EMF({V}_{R})$ in the ring change as:

In a fluorescent lamp choke (a small transformer) $100V$ of reverse voltage is produced when the choke current changes uniformly from $0.25A$ to $0$ in a duration of $0.025ms$ . The self-inductance of the choke (in $mH$ ) is estimated to be ________

A $LCR$ circuit behaves like a clamped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant $'{b}^{'},$ the correct equivalence would be:

An electric field $\vec{E}=4x\hat{i}-({y}^{2}+1)\hat{j}N/C$ passes through the box shown in figure. The flux of the electric field through surfaces $ABCD$ and $BCGF$ are marked as ${\phi }_{\text{I}}$ and ${\phi }_{\text{II}}$ respectively. The difference between $({\phi }_{I}-{\phi }_{II})$ is (in $N{m}^{2}/C$ ) ____________. 

Consider the force $F$ on a charge '$q$' due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$, if '$q$' is placed at distance $r$ from the centre of the shell?

A charged particle of mass ‘ $m$ ’ and charge ‘ $q$ ’ moving under the influence of uniform electric field $\vec{\text{E}}\hat{i}$ and a uniform magnetic field $\vec{\text{B}}\hat{k}$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $v\vec{i}$ and $-2v\vec{j}$ . Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale)  $(A)$ $E=\frac{3}{2}(\frac{m{v}^{2}}{qa})$ $(B)$ Rate of work done by the electric field at P is $\frac{3}{2}(\frac{m{v}^{3}}{a})$ $(C)$ Rate of work done by both the fields at Q is zero $(D)$ The difference between the magnitude of angular momentum of the particle at P and Q is $2mav$ .

A two point charges $4q$ and $–q$ are fixed on the $x$ -axis at $x=\frac{-d}{2}$ and $x=\frac{d}{2}$, respectively. If the third point charge ‘$q$ ’ is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will: 

Two identical capacitors $A$ and $B,$ charged to the same potential $5V$ are connected in two different circuits as shown below at time $t=0.$ If the charge on capacitors $A$ and $B$ at time $t=CR$ is ${Q}_{A}$ and ${Q}_{B}$ respectively, then (Here $e$ is the base of natural logarithm) 

Four resistances of $15\Omega ,12\Omega ,4\Omega$ and $10\Omega$ respectively in cyclic order to form Wheatstone’s network. The resistance that is to be connected in parallel with the resistance of $10\Omega$ to balance the network is ______________ $\Omega .$

An iron rod of volume ${10}^{-3}{m}^{3}$ and relative permeability $1000$ is placed as core in a solenoid with$10\mathrm{turns}{\mathrm{cm}}^{-1}$ . If a current of $0.5A$ is passed through the solenoid, then the magnetic moment of the rod will be :

In the figure, potential difference between $A$ and $B$ is: 

In the circuit shown in the figure, the total charge is $750\mu C$ and the voltage across capacitor ${C}_{2}$ is $20V$. Then the charge on capacitor ${C}_{2}$ is : 

A plane electromagnetic wave, has frequency of $2.0\times {10}^{10}\mathrm{Hz}$ and its energy density is $1.02\times {10}^{-8}J{m}^{-3}$ in vacuum. The amplitude of the magnetic field of the wave is close to $(\frac{1}{4{\pi \epsilon }_{0}}=9\times {10}^{9}\frac{{\mathrm{Nm}}^{2}}{{C}^{2}})$ and speed of light $=3\times {10}^{8}m{s}^{-1}$.

A small circular loop of conducting wire has radius a and carries current $I.$ It is placed in a uniform magnetic field $B$ perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period $T.$ The mass of the loop is $m$ then:

A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic filed at the center of circle is: