Electromagnetism PYQ — Page 39

The circuit shown in the figure consists of a charged capacitor of capacity $3\mu F$ and a charge of $30\mu C.$ At time $t=0,$ when the key is closed, the value of current flowing through the $5M\Omega$ resistor is $x\mu A.$ The value of $x$ to the nearest integer is 

A conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure  Two resistors ${R}_{1}$ and ${R}_{2}$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$. The correct statement about the directions of induced currents ${I}_{1}$ and ${I}_{2}$ flowing through ${R}_{1}$ and ${R}_{2}$ respectively is :

Four identical rectangular plates with length, $l=2\mathrm{cm}$ and breadth, $b=\frac{3}{2}\mathrm{cm}$ are arranged as shown in figure. The equivalent capacitance between $A$ and $C$ is $\frac{x{\epsilon }_{0}}{d}.$ The value of $x$ is _______. (Round off to the Nearest Integer) 

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ? 

A conducting wire of length $l$, area of crosssection $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference $V$ is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be___

A cube of side $a$ has point charges $+Q$ located at each of its vertices except at the origin where the charge is $-Q.$ The electric field at the centre of cube is: 

Two ions having same mass have charges in the ratio $1:2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2:3$. The ratio of the radii of their circular trajectories is,

Intensity of sunlight is observed as $0.092{\mathrm{Wm}}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point ? $({\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2})$

For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is 

A plane electromagnetic wave of frequency $500\mathrm{MHz}$ is traveling in a vacuum along the $y-$direction. At a particular point in space and time, $\vec{B}=8.0\times {10}^{-8}\hat{z}T$. The value of the electric field at this point is:(speed of light $=3\times {10}^{8}{\mathrm{ms}}^{-1}$) $\hat{x},\hat{y},\hat{z}$ are unit vectors along $x,y$ and $z$ direction.

If $2.5\times {10}^{-6}N$ average force is exerted by a light wave on a non-reflecting surface of $30{\mathrm{cm}}^{2}$ area during $40\mathrm{min}$ of time span, the energy flux of light just before it falls on the surface is _______ $W{\mathrm{cm}}^{-2}.$(Round off to the Nearest Integer), (Assume complete absorption and normal incidence conditions are there)

Two ions of masses $4\mathrm{amu}$ and $16\mathrm{amu}$ have charges $+2e$ and $+3e$ respectively. These ions pass through the region of the constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then:

Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ is : 

A charge $q$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\vec{E}$ through the shaded area is: 

An $L.C.R.$ circuit contains resistance of $110\Omega$ and a supply of $220V$ at $300\mathrm{rad}{s}^{-1}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45^{\circ}$. If on the other hand, the only the inductor is removed the current leads by $45^{\circ}$ with the applied voltage. The $R.M.S.$ current flowing in the circuit will be:

The figure shows a circuit that contains four identical resistors with resistance $R=2.0\Omega ,$ two identical inductors with inductance $L=2.0\mathrm{mH}$ and an ideal battery with E.M.F. $E=9V.$ The current $i$ just after the switch $S$ is closed will be: 

The relative permittivity of distilled water is $81.$ The velocity of light in it will be: $($Given ${\mu }_{r}=1)$

The two thin coaxial rings, each of radius $a$ and having charges $+Q$ and $-Q$ respectively are separated by a distance of $s$. The potential difference between the centres of the two rings is :

In the given figure the magnetic flux through the loop increases according to the relation ${\phi }_{B}(t)=10{t}^{2}+20t$, where ${\phi }_{B}$ is in milliwebers and $t$ is in seconds. The magnitude of current through $R=2\Omega$ resistor at $t=5s$ is _____ $\mathrm{mA}.$ 

A uniform conducting wire of length is $24a,$ and resistance $R$ is wound up as a current carrying coil in the shape of an equilateral triangle of side $a$ and then in the form of a square of side $a$. The coil is connected to a voltage source ${V}_{0}.$ The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is $1:\sqrt{y}$ where $y$ is ____________.

Match List-I with List-II <table class="pyq-table"><tbody><tr><td></td><td>List-i</td><td></td><td>List-II</td></tr><tr><td>a</td><td>Phase difference between current and voltage in a purely resistive AC circuit</td><td>i</td><td>$\frac{\pi }{2};$ current leads voltage</td></tr><tr><td>b</td><td>Phase difference between current and voltage in a pure inductive AC circuit</td><td>ii</td><td>zero</td></tr><tr><td>c</td><td>Phase difference between current and voltage in a pure capacitive AC circuit</td><td>iii</td><td>$\frac{\pi }{2};$ current lags voltage</td></tr><tr><td>d</td><td>Phase difference between current and voltage in an LCR series circuit</td><td>iv</td><td>${\mathrm{tan}}^{-1}(\frac{{X}_{C}-{X}_{L}}{R})$</td></tr></tbody></table>Choose the most appropriate answer from the options given below :

A common transistor radio set requires $12V$ $(D.C.)$ for its operation. The $D.C.$ source is constructed by using a transformer and a rectifier circuit, which are operated at $220V$ $(A.C.)$ on standard domestic $A.C.$ supply. The number of turns of secondary coil are $24,$ then the number of turns of primary are

A parallel-plate capacitor with plate area $A$ has separation $d$ between the plates. Two dielectric slabs of dielectric constant ${K}_{1}$ and ${K}_{2}$ of same area $\frac{A}{2}$ and thickness $\frac{d}{2}$ are inserted in the space between the plates. The capacitance of the capacitor will be given by : 

Two short magnetic dipoles ${m}_{1}$ and ${m}_{2}$ each having magnetic moment of $1A{m}^{2}$ are placed at point $O$ and $P$ respectively. The distance between $OP$ is $1m$. The torque experienced by the magnetic dipole ${m}_{2}$ due to the presence of ${m}_{1}$ is $________\times {10}^{-7}Nm$