Electromagnetism PYQ — Page 55

Sunlight of intensity $50 W{m}^{-2}$is incident normally on the surface of a solar panel. Some part of incident energy ($25%$) is reflected from the surface and the rest is absorbed. The force exerted on $1 {m}^{2}$ surface area will be close to $(c=3\times {10}^{8}m{s}^{-1})$

Given below in the left column are different modes of communication using the kinds of waves given in the right column. <table class="pyq-table"><tbody><tr><th>(1) Optical Fibre Communication</th><th>(P) Ultrasound</th></tr><tr><td>(2) Radar</td><td>(Q) Infrared Light</td></tr><tr><td>(3) Sonar</td><td>(R) Microwaves</td></tr><tr><td>(4) Mobile Phones</td><td>(S) Radio Waves</td></tr></tbody></table> From the options given below, find the most appropriate match between entries in the left and the right column.

 In the above circuit, $C=\frac{ \sqrt{ 3 } }{2} \mu F, {R}_{2} =20 \Omega , L=\frac{ \sqrt{ 3 } }{ 10} H$ and ${R}_{1} =10 \Omega .$ Current in $L\text{-}{R}_{1}$ path is ${I}_{1}$ and in $C-{R}_{2}$ path it is ${I}_{2} .$ The voltage of AC source is given by, V=200 2  sin( 100 t ) volts. The phase difference between ${I}_{1}$ and ${I}_{2}$ is:

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is $a$ and distance of its centre from the wire is $d (d\gg a).$ If the loop applies a force $F$ on the wire then: 

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by $$ \overrightarrow{\mathrm{E}}=2 \hat{i}+3 \hat{j} ; \overrightarrow{\mathrm{B}}=4 \hat{j}+6 \hat{k} $$ The charged particle is shifted from the origin to the point $\mathrm{P}(x=1 ; y=1)$ along a straight path. The magnitude of the total work done is :

An electron, moving along the $x-$ axis with an initial energy of $100 eV,$ enters a region of magnetic field $\vec{B}=(1.5\times {10}^{-3} T)\hat{k}$ at S (see figure). The field extends between $x=0$ and $x=2 cm.$ The electron is detected at the point $Q$ on a screen placed $8 cm$ away from the point $S.$ The distance d between $P$ and $Q$ (on the screen) is: (electron’s charge $1.6\times {10}^{-19} C$ , mass of electron $=9.1\times {10}^{-31} kg$ ) 

Figure shows charge $(q)$ versus voltage $(V)$ graph for series and parallel combination of two given capacitors. The capacitances are: 

The resistive network shown below is connected to a $D.C.$ source of $16 V.$ The power consumed by the network is $4$ Watt. The value of $R$ is: 

In the circuit shown,  the switch $S_{1}$ is closed at time $t=0$ and the switch $S_{2}$ is kept open. At some later time $\left(\mathrm{t}_{0}\right)$, the switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed. the behaviour of the current I as a function of time ' $\mathrm{t}$ ' is given by:

A rectangular coil (Dimension $5 cm \times 2.5 cm$ ) with $100$ turns, carrying a current of $3 A$ in the clock-wise direction, is kept centered at the origin and in the $X-Z$ plane. A magnetic field of $1 T$ is applied along $X-axis$ . If the coil is tilted through $45^{\circ}$ about $Z-axis$ , then the torque on the coil is:

In the given circuit, the charge on $4 \mu F$ capacitor will be: 

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure:  What is the value of current at $t=4 s?$

Two electric dipoles, $A,$ $B$ with respective dipole moments $\vec{{d}_{A}}=-4qa\hat{i}$ and $\vec{{d}_{B}}=-2qa\hat{i}$ are placed on the $x$ -axis with a separation $R,$ as shown in the figure  The distance from $A$ at which both of them produce the same potential is:

An electromagnetic wave of intensity $50 \mathrm{Wm}^{-2}$ enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by :

A parallel plate capacitor with plates of area $1 {m}^{2}$ each, are at a separation of $0.1 m.$ If the electric field between the plates is $100 N/C,$ the magnitude of charge on each plate is: $( \text{Take} {\in }_{0} =8.85\times { 10}^{ -12} \frac{ {C}^{2} }{ N\text{-}{m}^{2} } )$

A Helmholtz coil has a pair of loops, each with $N$ turns and radius $R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at $P,$ midway between the centres $A$ and $C,$ is given by [Refer to figure given below]: 

An ideal capacitor of capacitance $0.2\mu F$ is charged to a potential difference of $10V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0.5\mathrm{mH}$. The current at a time when the potential difference across the capacitor is $5V$ is:

A plane polarized monochromatic EM wave is travelling a vacuum along $z$ direction such that at $\mathrm{t}=\mathrm{t}_1$ it is found that the electric field is zero at a spatial point $z_1$. The next zero that occurs in its neighbourhood is at $z_2$. The frequency of the electromagnetic wave is:

A Helmholtz coil has pair of loops, each with $N$ turns and radius $R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of magnetic field at $P$, midway between the centres $A$ and $C$, is given by (Refer to figure): 

A power transmission line feeds input power at$2300V$ to a step-down transformer with its primary windings having $4000$turns giving the output power at $230V$. If the current in the primary coil of the transformer is $5A$ and its efficiency is $90%$, the output current would be:

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is ${B}_{1}$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is ${B}_{2}$ . The ratio $\frac{{B}_{1}}{{B}_{2}}$ is:

Two batteries with e.m.f. $12V$ and $13V$ are connected in parallel across a load resistor of $10\Omega$. The internal resistance of the two batteries are $1\Omega$ and $2\Omega$ respectively. The voltage across the load lies between,

A parallel plate capacitor of capacitance $90\mathrm{pF}$ is connected to a battery of EMF $20V$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be:

A charge $Q$ is placed at a distance $\frac{a}{2}$ above the centre of a square surface of side length $a$. The electric flux through the square surface due to the charge would be?