Electromagnetism PYQ — Page 46

A plane electromagnetic wave of frequency $25GHz$ is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic filed is given by $\vec{B}=5\times {10}^{-8} \hat{j} T.$ The corresponding electric field $\vec{E}$ is (speed of light $=3\times {10}^{8} m{s}^{-1}$ )

In a building there are $15$ bulbs of $45W$ , $15$ bulbs of $100W,15$ small fans of $10W$ and $2$ heaters of $1kW$ . The voltage of electric main supply is $220V$ . The minimum fuse capacity (rated value) of the building will be:

A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2A$ and having radius $2\mathrm{cm}$ and another wire $B$, also bent in the shape of an arc of a circle, carrying a current of $3A$ and having radius of $4\text{ cm}$, are placed as shown in the figure. The ratio of the magnetic fields due to the wires $\text{A}$ and $\text{B}$ at the common centre $\text{O}$ is: 

A loop $ABCDEFA$ of straight edges has six corner points $A(0,0,0),B(5,0,0),C(5,5,0),D(0,5,0),E(0,5,5)$ and $F(0,0,5)$ . The magnetic field in this region is $\vec{B}=(3\hat{i}+4\hat{k})T$ . The quantity of flux through the loop $ABCDEFA$ (in $Wb$ ) is _____________

An emf of $20V$ is applied at time $t=0$ to a circuit containing in series $10mH$ inductor and $5\text{Ω}$ resistor. The ratio of the currents at time $t=\infty$ and at $t=40\text{s}$ is close to: (Take ${e}^{2}=7.389$ )

The electric field of a plane electromagnetic wave is given by $\vec{E}={E}_{0}(\hat{x}+\hat{y})\mathrm{sin}(kz-\omega t)$. Its magnetic field will be given by

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass ? (Curves are drawn schematically and are not to scale)

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

An electromagnetic wave has electric field amplitude E₀ and magnetic field amplitude B₀. The ratio E₀/B₀ is equal to:

Three charged particles $\text{A}, \text{B}$ and $\text{C}$ with charges $-4q,2q$ and $-2q$ are present on the circumference of a circle of radius $d.$ The charged particles $\text{A}, \text{C}$ and centre $\text{O}$ of the circle formed an equilateral triangle as shown in the figure. The electric field at the point $\text{O}$ is 

Concentric metallic hollow spheres of radii R and 4R hold charges ${Q}_{1}$ and ${Q}_{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V(R)-V(4R)$ is:

A small bar magnet is placed with its axis at ${30}^{o}$ with an external magnetic field of $0.06T$ experiences a torque of $0.018\mathrm{Nm}$. The minimum work required to rotate it from its stable to unstable equilibrium position is:

The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $\vec{E}={E}_{0}\mathrm{jcos}(\omega t-\mathrm{kx}).$ The magnetic field $\vec{B},$ at the moment $t=0$ is:

A $750\mathrm{Hz},20V(\mathrm{rms})$ source is connected to a resistance of $100\Omega ,$ an inductance of $0.1803H$ and a capacitance of $10\mu F$ all in series. The time in which the resistance (heat capacity $2J/^{\circ}C$ ) will get heated by $10^{\circ}C.$ (assume no loss of heat to the surroundings) is close to :

The correct match between the entries in column I and column II are : <table class="pyq-table"><tbody><tr><td></td><td>I</td><td></td><td>II</td></tr><tr><td></td><td>Radiation</td><td></td><td>Wavelength</td></tr><tr><td>a</td><td>Microwave</td><td>i</td><td>$100m$</td></tr><tr><td>b</td><td>Gamma rays</td><td>ii</td><td>${10}^{-15}m$</td></tr><tr><td>c</td><td>A.M. radio</td><td>iii</td><td>${10}^{-10}m$</td></tr><tr><td>d</td><td>X–rays</td><td>iv</td><td>${10}^{-3}m$</td></tr></tbody></table>

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}},$ with its polarization along the direction $\hat{k.}$ The correct form of the magnetic field of the wave would be (here ${B}_{0}$ is an appropriate constant):

A capacitor $C$ is fully charged with voltage ${V}_{0}$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$. The energy loss in the process after the charge is distributed between the two capacitors is :

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point $B$ with respect to the point $A$ is: 

At time $t=0$ magnetic field of $1000Gauss$ is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500Gauss,$ in the next $5s,$ then induced $EMF$ in the loop is: 

In $LC$ circuit the inductance $L=40\mathrm{mH}$ and capacitance $C=100\mu F.$ If a voltage $V(t)=10sin(314t)$ is applied to the circuit, the current in the circuit is given as:

A capacitor is made of two square plates each of side ‘ $a$ ’ making a very small angle $\alpha$ between them, as shown in figure. The capacitance will be close to: 

Consider four conducing materials copper, tungsten, mercury and aluminum with resistivity ${\rho }_{C},{\rho }_{T},{\rho }_{M}$ and ${\rho }_{A}$ respectively. Then :

A long, straight Wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and $2a$ , respectively from the axis of the wire is:

The electric field of a plane electromagnetic wave is given by $\vec{E}={E}_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\mathrm{cos}⁡(kz+\omega t)$ . At $t=0$ , a positively charged particle is at the point $(x,y,z)=(0,0,\frac{\pi }{k})$ . If its instantaneous velocity at $(t=0)$ is ${v}_{0}\hat{k}$ , the force acting on it due to the wave is: